My strategy for prepping for the season's PvP has been "get what gives me the most resil first", and I think that's an effective strategy when starting out as well. Big-ticket items like helm, chest, and shoulders will of course have heaps of resilience. HOWEVER, if you're starting out, nothing is more important than a trinket to get you out of snares and stuns

To reiterate:
PvP trinket, then whatever has the most resilience.

Simply my opinion... Given the scenario you described, your first and foremost priority is to get as much resilience as you can. More resilience = more surviability and less frustration for you in the short term as you get better PVP gear over the long term.

Trinkets, relics, rings, and neck pieces are usually the least expensive way to start getting resilience. (Current season honor gear trinkets will net you over 400 resilience a piece!) In fact, one of the first pieces you get should be the "updated" Insignia of the Alliance/Horde trinket (the one you can use to remove all movement impairing or loss of control effects on your character). After filling those slots, start saving for the main set pieces.

Also remember that you can run REGULAR random and Heroic random dungeons to get Justice and Valor points...at the Justice/Valor trade goods vendor, you can then exchange those points into Honor/Conquest (with about a 100 point exchange fee for the Justice to Honor conversion).

Finally, as an addendum to Gray's "Don't fight on the road" advice, remember that some BGs give more Honor to folks who stay and defend objectives. In such BGs, I'm usually in the top 3 or 4 for honor earned--not because I'm killing everyone, but because I'm defending objectives/nodes.

Hope this helps; good luck!

This is what I did as a Shadow Priest, but the general approach should work for anybody. Basically, Resilience should be the first priority for almost anybody, and you'll get more resilience at a lower cost by replacing PvE gear with PvP gear before worrying about upgrades to your current PvP gear.

1. Acquire a set of ilevel 377 Vicious gear (crafted by tailors, leatherworkers, or blacksmiths; on my server, it's about 2,000g to make, not counting training costs, or 3,000g to buy on the Auction House).

2. Buy Vicious rings on the Auction House (Jewelcrafted, I believe; I got two rings at 200g each). Gem and enchant your gear; best-in-slot would be nice, but second-best gems and enchants are affordable and should do well enough for now.

This should be enough to get you into Battlegrounds without constantly having to cower behind somebody else. Just the same, stick with the pack and avoid one-on-one confrontations for now.

3. Buy trinkets and a necklace with Honor Points. When people use say "PvP trinket" without qualification, they're probably talking about the ones that you can Use to release all movement-impairing effects. Snares and roots are a huge part of PvP, so this trinket should probably be your first purchase, unless you're Human or maybe Gnomish; the cheapest one's only 55 Honor, but better ones offer stat bonuses as well.

4. Once you've earned 7,250 Honor (you don't have to have that much on hand, you just have to have earned that much since 4.3 hit), you can buy PvP weapons. These aren't that different from normal weapons, except they offer even more Resilience. Some combination of main hand, offhand/shield, and ranged/relic/wand should give you another 300 Resilience, putting you around 3,500.

(Note: I completed steps 1-4 in two weekends of Holiday Battleground grinding. You could probably do it faster.)

From here on, use Honor and Conquest points to improve upon your current gear. The Resilience difference between level 377, 390, and 403 gear isn't that big, but each step offers respectable increases in your main stats (Stamina and Str/Int/Agi). You'll get 100 Conquest points for your first random or holiday win of the day, and 50 Conquest thereafter, so keep an eye on that; you just might get enough Conquest for an additional upgrade. You'll probably hold onto this stuff for a while, so this is where you'd start applying the expensive enchants.

Each class has at least one five-piece PvP armor set: hands, head, legs, shoulders, and chest. Set bonuses are granted at 2 and 4 pieces; the two-piece bonus is even more resilience and a boost to your primary stat, so your next two upgrades should probably be aimed at getting that bonus. Heal-capable classes will likely have two sets, one for healing and one for DPS; you can tell them apart by the material, like Satin (DPS) and Mooncloth (Heal) for Priests, or Linked (DPS) and Mail (Heal) for Shaman. Ruthless Gladiator (ilvl 390) and Cataclysmic Gladiator (ilvl 403) gear will both count for set bonus purposes, provided they're the same "material".

You can't access the weapons until you've earned 7250 honor in the current season, so those will have to be further down your list. I would pick up the PvP trinket (Gladiator's Medallion) first, so you can break free of stuns/roots/snares at critical moments. Then I would get the main armor (head/shoulders/chest/hands/legs) to pick up the set bonuses. I usually get the hands, then shoulders, as are they're 1650 honor apiece compared to 2200 each for the head/chest/legs. Then fill out the rest of the accessories as you go. Also bear in mind that you can buy the head and shoulder enchants with Tol Barad Commendations in addition to honor.

Once you have your freedom trinket make sure to get hands first. This is because the hands piece usually has a nice PVP specific bonus. Beyond that buy what vicious gear (crafted) you can off the AH and then go after your remaining pve pieces prioritizing with an eye towards whatever gets you the most resil for the least honor first.