The main goal at this stage is to level up.  And if this is your first character, to enjoy your introduction to a new game!
At this stage, you are mainly focused on the following areas:
* advancing the personal story
* killing relatively easy monsters
* gathering craft materials (eg iron ore nodes)
* exploring the map (tagging waypoints, uncovering new map areas, points of interest, vistas)
None of these are particularly demanding in terms of gear. So don't sweat the gear much at this stage.

However, some small attention to gear will make your leveling go more smoothly.  Identify the high damage weapons of your class. Support/defensive items have their place, but when leveling generally you just want to kill things as fast as possible. For example, you'll kill things a lot faster on guardian if you use greatsword/sword as opposed to say mace/staff.

As far as gear goes, get blue (fine) or green (masterwork) gear.  Yellow (rare) gear is not worth it at this stage given how often you'll be replacing gear.  Try to keep your gear level within 5-10 levels of your level.  You can "live off the land", craft it, or buy it on the trading post.  Don't spend too much on it, since you will frequently be replacing it. I usually salvaged it after I was done with it, but if the gear is blue you can resell or hand down to another character.  But given the expense of cloth materials these days, salvaging light armor is often the way to go.

Try to make guild missions (we run them twice a week, but you only get credit once.  You will get decent loot and gold, and you can stock up on guild commendations (which are used to buy top tier accessories for lvl 80).
You may be too low level to do all the missions.  For most of them we will know a couple hours in advance, so ask in guild chat or teamspeak whether you'll be able to do them at your level and check whether you have the right waypoints (and get them in advance if you don't have them, making tens of people wait for you to run to a waypoint is rude!)
Note that guild missions aren't very good for leveling, and you don't really need the commendations until lvl 80.  So don't fret if you can't do them all every week.

On a side note, WvW is another option for leveling, but bear in mind you will be less effective than a fully geared 80.  At lvl 35+, in theory you can do dungeons to get xp. In practice, however, you will have a hard time getting groups to do dungeons when you are low level (a lvl 80 with good gear is going to be a lot more effective even after they are down scaled for the dungeon lvl).