Buy a mog sack for 9,999gil
Learn to macro in gear/spells/job abilities etc.
Make friends, but dont ask the same ones repeatedly for help spread the wealth around
Try to do things at least once or twice on your own first, if its a quest and you need help do everything you can do first solo, before asking for help. People will help more often if your prepared, use wiki to get the info you need about what you want, and have the key items ready from when you solo. Example is the nation rank quests. I love to help people, I hate to have my time wasted. I come to help someone and they don't have all their key items ready before a fight that they need my help on pisses me off. That's why you need to solo what you can, people are understandable if you didnt get a key item or drop that you can't solo but nobody wants to wait around for you to either get the cs you need still before the fight or ask a million questions because you don't have wiki access. Use the pulblic library if need be and print out your lists in advance.
Read wiki about level cap quests (after 50 you will need to do these quests every 5 levels to break the next cap) and prepare for them.
Look into the goobie bag quests, your "fame", and mog locker.
There's also many areas you need access to first, before you can explore them: shadowreign areas from wings of the goddess add-on, abyssea, sea, sky, aht urhgan whitegate from treasures of aht urhgan
First priority should be leveling your character and sub job(s) to cap, currently 95. This will enable you to do many more things easier than at lower levels and open the door for other things to you.
Gear: I recommend not spending much gil on gear, untill you hit cap (currently 95). Get yourself a decent weapon for whatever level you currently are at, and that's it. there are a few rings and such that may benefit you earlier, but as a new player your more likely to buy the wrong one and waste your hard fought gil, so just suffer for the time being or buy cheap gear that fits a purpose. Check other players, talk to people, see what is good for that job at higher levels. The goal is not to buy for today, buy for tomorrow because xp is fast in this game now and gear gets outdated even faster before you hit cap. Once you hit 75, start a magian trail for a weapon that you are interested in doing. Again, ask around to see what is worth it some weapons are junk while others outshine. It may be a little to early to ask yourself this, but consider an empyrean weapon or just build something to get you thru until you are established then you can start your empyrean weapon (explained more below). Once you hit 78, you will have access to perle, teal, and aurore gear sets. These are cheap and decent gear. You can buy off AH or from npc in abyssea with cruor (abyssea currency).
You can then start working on your empyrean armor (af3) post 78, or sooner if the oppurtunity arises.
You can do artifact armor and weapon(af1), starting at 40 for most jobs, but because xp is so fast these gear peices are often outdated and not worth time investment. However, talk with decent higher level players, some af1 is still great macro peices. for certain jobs and can not be replaced. Once you have 78+, start trying dynamis in your spare time. There you will get ancient currency that can be bazaared for gil and relic armor (af2). Relic armor is mostly for your macro sets, but each peice and job are different. Like af1, some is outdated while other peices are impossible to replace.
XP: Ok, at low levels (10-29) the best places for experience points is alliance style fights in gusgen tunnels (level cap 10-20) or crawler's nest (no clue on the best cap there i've had all my jobs past 30 a long time and burn in abyssea). There are many zones that offer the same xp, the trick is finding a zone that has alot of level sync'd people and a field of valor or grounds of valor book. The trick is to get a page from the book and spam the mobs listed there to get the extra xp called "book buring". Just try those two zones first, turn your party flag on, and shout for a party or ask the leader of a group if you can join.
Abyssea XP: First, unless somebody knows you or pities you, odds are your not going to be leeching in abyssea unless you have a 70-75+ dd (damage dealer) job or magic damage dealing job, a whm with cure 4+ (42), or a rdm 55+ (cure 4) or similarly leveled sch with cure4 (not sure when they get their cure4). Or without a few hundred thiousand gil to pay someone to let you leech their party. To leech a abyssea party generally you need meet one of three requirements: 1. you are of job and level as stated above, 2. you have cruor so you can "key", this means you will be opening chests for the party in exchange for leeching rights. You need cruor to buy the keys though, and so its a catch 22, as you need already have been to abyssea long enough to get cruor or have a 75+ job to do voidwatch to get cruor from there, 3. start you own abyssea party and leech your own party. I DO NOT recommend or like new players that host abyssea xp pt's, the reason is most new players do not understand enough of the pt makeup and lights in order to host a successful party. I suggest that during your first abyssea party that you do not host you ask questions and learn about abyssea so later on you can host your own party. Keep in mind people rememeber lamers in this game and a bad party can ruin you fast in the eyes of other players. That said, abyssea is the best place for xp, period. Perhaps, as was suggested earlier, leveling whm for your first job would be most beneficial to you. You can leech to cap asap in abyssea at 42 with cure 4, and as explained latter you can get more invites for empyrean armor +1/2 farming and empyrean weapon items.
Abyssea empyrean armor/proc: Ok, this is the other reason people are in abyssea, the gear. First, you need understand about proc (process weakness). Since abyssea, SE has used proc in other area as well, so keep in mind dynamis now has proc, as does voidwatch (VW). For abyssea, there are three proc, blue, red, and yellow. Wiki explains the difference, but what yuou need to know is if a party does process a Notorious Monster's weakness, then the drop rate is increased for the corrisponding weakness. What that means is, most people dont just go kill notorious monsters (nm), they go to proc the nm first, then kill it. In the case of +1 armor items, four different +1 drop from the same nm. Becaue of this, most +1 parties are made up of no more than 4 people, because each persopn rather lot a single +1 and have the party agree beforehand that that +1 is theirs. Four people, four different +1, get it. Now to proc +1/+2 drops, magic weakness must be triggered. this can be done with any sub job nin, a whm, a blm, a blu, and a sub job bard. While rdm and sch can proc yellow for magic weakness, they lack the spells that whm and blm have and so they are not as often invited. Add the cure power of a whm and its easier to understand why whm is suggested as your first job to cap.
Abyssea empyrean weapons: not gonna be long here. Point is they take alot of time and work to get, but are attenable for the average player with a just a few friends that are dedicated to results. Once you been around the block a few times you'll know how to proc weakness and you will have a better idea if empyrean weapons are your thing. You will prefer to have a thf, war, nin, whm at the least, and most likely add a blm to your unit. Larger groups use other jobs such as cor with empyrean gun to cap amber fast and brew speed kill, or a blu to solo burn chests/te/etc. Some nin's can straight solo some hnm in abyssea with the right atma/gear, I personally dual box mine so many combo's work but i listed the pt size for farming empyrean weapons as about 3-5/6 on average to give you an idea of the amount of people you will need. Note, these 3-5/6 would have good atma and experience to be successful at low manning but once you get the hang of things you'll do fine. Read wiki about atma.
Try these websites
ffxiah.com
gamerescape.com
http://wiki.bluegartr.com/bg
http://wiki.ffxiclopedia.org/wiki/Main_Page
www.ffxi-atlas.com/
http://ffxi.allakhazam.com/
Moghouse: There's a few quests related to furniture which will increase your mog safe storage to 80, also you can purchase furnature to put in your mogsafe that gives you access to mogstorage (again 80 cap and only available in your home nation) For mog storage I suggest when you can afford one get a
Panetiere. Also, look into moglocker and if you've been on for a few months and are gonna stay grab a mogsachel from the mogtoken ($9.99, mine has lasted me a few years now).
Travel: This one is big. 1. Start doing supply quests to get yourself outpost (op) access from the npc in your home nation. 2. Depending on supekupor power, teleport moogles maybe available for transport to the cities and selbina/mhuara. 3. Get all the telepoint crystals and recall crystals. 4. Get access to all the abyssea maws asap, even if you can't get a party (pt) just visit them to uinlock the maw and cutscene (cs) associated with each of the 9 abyssea zones so that you may warp to them. 5. Chocobo license, 6. once you attain 75+ speak to the voidwatch npc's in the 3 cities and get you key items to do those events. Even if you don't do VW, you can at the least use the npc's in the cities and other locations to teleport you to certain areas of the game. Theres other travel, but this is the main stuff and fastest.
Keep track of stuff: at the least, write down what boss and caturea nm clears you have from abyssea, and what op's you have if you can't remember. For abyssea you are gonna want these clears and all merit, furtherance, lunar, sojourn, and celerity abyssites asap. Ask around about atma and what ones are best for which jobs.
Gil: once you are using abyssea regularly you can convert cruor by buying chocobo blinkers (see wiki) or the three gear sets (perle teal etc) and selling this to npc's in vanadiel. Mind you that eventually you will need cruor to buy brew in abyssea but this will get you past the hump. You can also farm dynamis once you get the hang of things.
Hope this helps, goodluck and don't be discouraged.