Where to farm
Keshatta is THE only viable place in AOC to farm pvp xp and level up within reasonable time. Accept this and move on.

Minigames
As for now (1.4 build) minigames are horrible for pvp xp and usually packed with premade groups consisting mostly of casters and healers (or both: TOSes). Do not run minigames because they are waste of time. This could change in the future.

How much pvp xp you will need
Getting from lvl 0 to lvl 2 is a breeze.
It takes 72.000 xp to gain lvl 3, 148.000 xp to get to lvl 4 and whooping 232.000 xp to achieve lvl 5. Thats is just shitload of pvp xp. In order to ammass such great ammount of pvp xp you will need a strategy and dedication: a lot of both

Farming strategy
If you are not "teh hardcorez" like me (job, home life, chores, walking the dog, cooking and all that crap) you can probably pull 1-2 hours of gameplay a day (3h if you are lucky). That time must be spent wisely. Follow these tips for best results:

rule #1 "Set a daily ammount of pvp xp to gain"
This might sound like a very basic stuff, but trust me: the ammount of xp you will need is overwhelming. You need to "cut" the progress bar into tiny little pices and "climb the ladder". Setting ammount of xp to grind will give you a

sence of daily achievment and a slow, but steady progress. I went with following:

1) 1.000 xp - this is what you need daily. Its a reasonable ammount and its a breeze to farm. Let's do a little math: 148.000 : 1.000 = 148 days which is 5 months. Sounds horrible? Yes, but you will level up eventually.

2) 2.000 xp - not every day in Kesh is the same, somedays it's easier, someday its hard as nails to get kills (especially when zergs are tighly packed and close to guards, or there are lots of lots of soliders and healers). If the first 1000 xp is easy to get, pull another 1.000 to get a "boost". Lets do the math:

Lets assume that only 1/3 of your days in Kesh are "good days" when you can get 2.000 xp
that means: ~50.000 xp will be gained at 2.000 xp speed. So 50.000:2000= 25 days. Thats like a month. 5 months - 1 month = you have just cutted a whole 30 days of grind out of your schedule.

3) 3.000 xp - those will be rare, but still can be done. Let's assume that only 1/5th of your time in Kesh will grant you such a gain. Lets do the math:

148.000:5 = ~30.000 xp that means that you will do that ammount in 10 days

5 months - 35 days = 3 months and something. Now that is reasonable.

Can you get more than 3.000 xp in Kesh in one day? Hell yeah! Will you have time to get more than that? Its up to you.

rule #2 keep it reasonable
Farming pvp xp is a tiresome and at times can be boring. Do not overdo your farming sesions because you will crash and burn. Rather can half-killing yourself in order to farm 5k xp in one day and then not play for 4 days, go for easy wins with steady 1k xp pace with occasional 2k boost.

rule #3 keep the kill/death ratio out of Kesh
I will never understand people that care for their K/D stats. I have 7470 kills and 7420 deaths. So what? It only shows that I worked hard for my level and that I have killed more times that being killed. When you are doing solo or 2 man group pvp YOU-WILL-DIE, a lot. For every kill you make you will most likely die as zerg members gang up on you. There is nothing you can do when you get instantly KB, feared, stuned and charged by 5 people at the same time.
Even if you go so low as for running to the guards, they will pull the guards and then deal with you. Accept that you K/D ratio goes to shitter and move on.

rule #4 set a goals
Do not look at your progress bar as a whole - its depressing. Instead aim for getting 10.000 xp chunks. Your goal is to get another chunk of pvp xp and press on. Getting to lvl4 takes 1480 clean kills (target gives 100 xp), if you look at it this way you may aswell just quit now.