If you're not playing in a squad or outfit, e.g. if you're soloing:
For goals, if you're not playing with a group, you can take the little one to three capture point outposts and such, claiming them for your faction. They are rarely defended. If they are, it's usually easier to just take off and fly to another one than to bother fighting the guy there since most are undefended because there's no benefit to sitting at a base twiddling your thumbs. Taking outposts weakens nearby bases, making them easier for your faction to capture them, as well as taking away resource production from whoever owned the outpost previously, and giving it to your faction instead. You can also participate in larger battles for auraxium bases and the like, but if you lose all the surrounding outposts you will likely lose the battle as well, and conversely if you capture them all you can win more easily since surrounding bases/outposts affect the outcome of the 'ticket race'.
I would suggest getting in a fighter and practicing flying it around a bit near the warpgate (without trying to land, and not near the places where planes spawn), then once you have some practice with controlling it in the air, see if you can land on a flat surface. It may take some practice, as you may explode a few times (I definitely did). Waiting until you have 750 of the green resources helps, and a large income of them, and the fighter 5-minute implant to let you try again more quickly. At some point they need to add a simulation / VR mode, I think.
You'll find that they like to tip over and explode on landing and takeoff if you land on the edges of buildings, on non-flat terrain, or too close to structures, especially if you are unable to prevent them from doing so (but there are positions that it's just impossible to take off from, like when you land directly facing a tower with one wing caught on it), but planes are basically the quickest way to get anywhere on the map. I've also seen the landing gear cause a reaver to tip over when it extends, which was facepalmworthy and almost made me wish I was flying a scythe instead (they don't have landing gear and are rather flat). The in-game store has implants which will reduce the re-purchase time on particular vehicles to 5 minutes for 25 auraxium for a 24 hour duration, which is quite cheap as you can get that much for being online for 5 minutes if your faction has 3 or more auraxium bases (each one is 10 aurax per 5 minutes). So you can for instance get the one for the reaver (fighter), or the one for the vanguard (tank), or the one for the galaxy (aerial transport), etc. There are 50 aurax ones that operate on two vehicles instead of one. The main issue with the vehicles then becomes having enough resources to repeatedly buy them.
There are two ways to use airplanes to get places: Either buy a vehicle and drive/fly it somewhere, land it, take the place, get back in, and go somewhere else, or just ditch it in the air and hop out. In practice hopping out in the air is unsafe unless you're in a galaxy or you're moving slow and over land (or an LA as they have jetpacks, although I've still died from horizontal movement speed as an LA despite using my jetpack). It's better if you can land it, and if it starts to tip over when you land you may just have to jump out, as when they explode from flipping over they generally won't harm anyone standing nearby for whatever reason.
As an alternative, you can drive ground vehicles to places instead. The flash is a small quad bike, and extremely cheap, but it has traction issues and seems like it doesn't have 4WD right now. Basically it can't go up hills effectively. There are also tanks. They're slower than aircraft, and not safe if there are enough aircraft around. You also have to be RIDICULOUSLY CAREFUL if you're driving a tank, not to be moving, at all, anytime any friendly infantry are anywhere near you, which includes ones that you can't see. Meaning you have to constantly watch the minimap. If someone so much as walks next to your tank while you're driving they WILL die right now, and you'll get blamed for it. Or if they run in front of you and you are unable to stop in time. Or if they drive a jeep into your tank and die. And so on. If this happens enough you'll get weapons-locked for a while. I've managed not to be weapons locked yet by (a) being spectacularly careful about driving around when in tanks, and (b) mainly playing on a rather underpopulated server.
Edit: Is it just my first few landings with the mossie going horribly wrong, or is the mosquito even more prone to tipping over (this time forward, over the nose) than the reaver? The hilarious thing is that each time it was stationary (with the nose pointed at the ground... what) before I got out, then flipped onto its back and exploded as soon as I got out.
I'd remove station name from that. Maybe allow your PS2 forum name, but station name is your account logon and should really be something different from your characters and forum name to help secure your account. Less vital for a F2P like PS2, but still good practice.
That is exactly why I didn't enter mine in there.