Almost every mat you need for crafting lv 20 items and below can be bought at a vendor; so while cheaper to farm it, you by no means need to hold onto it if your inventory space is nearly full. Sell what you don't need and buy/farm it later, trust me its far simpler that way.

For fishing bait, invest in the Freshwater and Saltwater Boilie bait. Its an all purpose bait that can be used instead of the more specific baits. While it doesn't work on all fish, by the time you're fishing for those you should have access to retainer and saddlebag inventories which will ease the storage burden for you.

Regarding inventory space and the developers, they feel it as much as we do. Imagine the database like a completed 10,000 piece puzzle, then remove 1000 pieces at random. Those removed pieces are where they can put things like extra inventory but then they have to figure out how to link it all together in a way that works smoothly and doesn't eat too many server resources or cause extra data to be sent between the client and server unnecessarily. They also have apolicy where all of your character data must be synced with the server every few seconds (10 seconds if I remember correctly). Even a minor increase of data per character will have a massive impact on network and server loads and its something Yoshi has been reluctant to even consider changing.

In short, its a lot of expensive and time consuming work; they know its an issue but it hasn't reached that critical mass where it becomes worth the cost of doing the overhaul.

When it comes to leveling, what I see many do is level one or two jobs with the msq and leave the side quests for a couple other jobs. You're going to get so much xp you'll out level the msq quickly if you only play one job. You also get a bonus to leveling any job lower than the highest level job you have, so they'll all level faster than the first time which helps make up for the lack of msq quests on alt jobs. Jobs in the same role (Melee DPS/Ranged DPS/Caster/Healer/Tank) share gear, so ifyou're leveling 2 tanks at the same time, you don't need to worry about buying extra gear aside from the weapons.

I would also advise not worrying much about HQ gear while leveling under 60. Not only is the HQ gear more expensive, you'll also be replacing it every few days as you level, its just not worth it really. You can buy any NQ LV 60 gear and below from vendors so you don't need to worry about MB price inflation and dungeon drops will server you just as well.

Hope that helps. Welcome to Eorzea.