About the "getting gear" that a few people have mentioned (and in case you don't know)... since you are lvl 20ish right now, there is no special PvP gear. I think until level 40 (?) you can't get anything that has "Expertise" on it, which is the PvP stat that you want. So until then any gear you can get will be the same as your PvE gear.
That said, there are PvP vendors on the fleet that you can use. You can buy a "PvP" armor set at level 20. In my opinion, it's a pretty good deal, because it costs commendations, instead of credits, and if you PvP a lot you should have plenty of comms by then. But there's nothing "PvP ish" about it except its name. At level 40 there is another set, and that one I think includes a bit of expertise. There is another vendor you can buy "PvP" weapons from (near the quest terminals). Again, cost is comms instead of credits, so if you have lots of extra comms feel free to buy (but see about saving up comms below). Note that all these pre-50 "PvP" sets are tossed aside as soon as you ding 50.
Once you ding 50 you throw all the previous stuff out (give to lower level alts, or to companions), and throw on the free set of "recruit" gear you'll get. And *NOW* is when the gear grind begins. (The exact gear grind is, apparently, about to change with update 1.6 - but I'm sure there still will be one.
) Whatever the grind is will certainly involve spending "warzone commendations" and "ranked warzone commendations". You can save several thousand of each of these (ranked ones starting at level 40). Plan to do so (save as many as you can - maxing out your "bank" of them if you play enough sub-50 PvP), and then when you ding 50 you will be able to get some post-recruit gear right away. You can look for previous topics about what gear to get in what order.