Where do I go to buy armor or crafting materials and recipe

ATM, I am a rank 12 Pugilist and am have a tough time killing Light Blue enemies... so i got this crazy idea in my head that, "Hey, I need new armor and weapon!" but from what i can tell, things arent that simple, i'm running around for an armor vendor... none to be found (excluding the boot vendor in Gridania) so i thought i'd try to craft some new armor, but the recipes arent available until im allowed guild marks... so how does one get new armor and weapon? Please enlighen me...
(only have access to Gridania)

Well there are NPC's in the market wards that sell armor and weapons for rank 1-20 but it's not cheap. Gridiana on most servers is a ghost town with noboby there, seems on most servers Ul'dah is the best place to be and it you will have the best chance of buying gear from the wards as they are always much busier than the other cities.

My advice would be get a rank 15ish weapon and rank 20ish gear you willlevel into it son enough and as you level so fast it is reall not worth buying the low level gear because of how fast you rank up.

Hey hey.

I'm not sure about buying or not buying low-level gear, but as far as recipes go, you don't actually have to learn them. You can look them up on the Zam or Eorzeapedia wikis. Certain recipes will recommend a given type of training, which is what you buy with guild marks, but it is by no means required, especially at lower levels. If it requires facilities, just talk to the repair NPC as the required crafting profession and select "I'd like to perform my own repairs" (paraphrased; I'm not logged in at the moment to get it verbatim).

Then from your menu, select Synthesize, add your ingredients, and go from there! Good luck!

Oh, also, Ul'dah does seem to be The Place To Shop. The run there is lengthy, but not terribly fraught with danger. Just follow the road south (a long long time, heheh) until you get to the next zone, and then follow the road west in the next zone. Ul'dah is south-central of that zone (Thanalan).

If, by some odd chance, you're on Wutai, I have a pair of Dodoskin Cesti I just outgrew and can make you PGL armor.