-Personally I'd avoid using up too many guildleves while your level is low. Do the tutorial one, maybe a couple of the first ones for gil, and then regularly check the guildleve counter to see if they have gear/weapon rewards, but don't spam them for exp until you're a little higher, until you get sick of grinding, or until you have so many guildleve allowances that you'll never run out. Another option is using up your initial Guardian's favor before listening to this paragraph.
-Exping: A lot of enemies are clumped together in large groups. Find one of these groups and kill the critters non-stop for exp. If you target something like sheep (right outside Limsa-Lominsa) or marmots (right outside Ul'dah and Gridania), you should be able to make some money at the same time. When your exp gets crappy and low, just walk alongside the road until you find a higher group of enemies (go north from Limsa, west from Gridania, east from Ul'dah).
-EXP parties are usually made in Ul'dah, but depending on your server these might be rare or might never happen below level 35. There's a LFG system that's not widely used (in my server), but you should try your luck and use it as there's no downside to flagging yourself for exp (you can lfg as any of your classes). How to do this: Menu > Search > Your Settings > Seek Party & Choose Class > Close.
-Sidequests are a pretty good source of gear and money early on, but some of them require you to walk all over the place, which you might or might not find annoying before getting your chocobo or unlocking aetheryte crystals.
-Class hierarchy seems to change every patch and there's a new update coming in 3 weeks, so although currently the damage dealers that people want are Thaumaturge and Archer, things could change soon.
If you asked because you want to play it safe with your first class, do Conjurer. As Conjurer you should be wanted in every event in the foreseeable future (since there's no other healing class in the game). It's also pretty good at solo-leveling, so your quality of life should be acceptable.
-Some useful skills (especially for soloing and playing early on) are Second Wind (Pugilist lv.6), Cure (Conjurer lv.2), Bloodbath (Marauder lv.6), Invigorate (Lancer lv.4). Later on there's Sentinel (Gladiator lv.22), Raise (Conjurer lv.18 ) and Chameleon (Archer lv.42). You can get most cross-class skills if you get all classes to 33ish, which you'll probably end up doing eventually.
-If you have any interest in disciplines of the hand, have a lot of movies/series ready to watch.
-Don't worry too much about which specific stats your gear has while you're leveling (up to level 35-40 or so), just make sure to wear gear that's level/class-appropriate for you.
-Lastly and most importantly, if possible, make sure to choose a server with friends in it. Leveling multiple classes will become infinitely easier if you have friends willing to lend a hand (also known as PLing your character to max level in a weekend).