I played it a couple times when I start a 1.5 years ago, and a few more past few days.
I thought rengar would be good because he was good in that Shurima special event, but i did poorly with him. Same with Jax and Evelyn. Did decent with Cho.
How many tanks/mages/dps champs do you want on a a team?
I believe that this site has your answer: http://www.lolpro.com/guides/game-play/1434-game-play-guide-dominion/common-mistakes it hasn't been updated in a while so it doesn't include some of the more recent champs, but it's a great place to start.
It's usually good to have at least 1 AD and 1 AP champ going top that can do good damage, but comps can vary quite a bit. Main thing is to control the jungle, stick together as a team, and remember that you can gank bot (though the jungle)
From my experience with co-op vs Ai. A lot of tanks (we're talking 3 traditional tank + a tanky mage here) is really hard to beat. Because they take so long time to kill without a real tankbuster.
Other than that? I'd say that good duelists are good on dominion, because usually you won't get grouped on as badly. Jax should be good. Fiora is good. One of my personal favourites is Irelia.
Al of it for vs bots though. So keep that in mind.
one strong bottom laner (good duelist or zoner, good waveclear, good at dealing with ganks) one tank then some mix of damage and support that works well together
Ya gotta have this armordillo man.
Old men 
also work, or so I've heard
Start with bot. A good bot is hard to explain, since many things can work. Basically you need to balance out 2 things as a bot laner: the ability to win, and the ability to not lose. Winning means your ability to push, punish, and bully the other bot. It's your offensive dueling power. Not losing is your safety. Whether through sustain, tankiness, zoning range, etc. Stay safe, and make sure you don't instantly die to ganks.
As for top, make sure you have a good initiator. It doesn't HAVE to be a tank, but Leona is a good starting point. J4 also works amazingly. As long as you have enough bulk and CC, and can force an opponent into a full fight, you're good. On top of that, you generally want one good mobile assassin or bruiser to quickly burst down the biggest threats, a mage with good AoE damage, and a support. And by support, I mean has lots of buffs and utility to make your team do better. Not SR's crap idea of has no gold and sucks all the time. Scouting tools are great if you have them. Any sort of skillshot or other vision aid to check bushes for you from a safe distance.
Itemization focuses mostly on penetration early. Vision items are also important, as they prevent facechecking in crucial moments, and relaly help you to control the jungle. Spookyghosts are a must on your mage or support.
As for gameplay, the idea is mostly to control the jungle, and use it to move between points as needed. Figure out where your opponents are, what they are doing, and what they can react to. Hit them where they can't defend. Gank bot whenever you can spare to. If they are going hard for top, back cap. Just make sure you move together as a group, splitting off only when needed while the main group engages somewhere. If you can catch somebody out alone, you earn a massive advantage for the time they are dead.
Don'ts: Do not push lanes. Avoid moving through them as much as possible. If anything, kill 1 super minion to allow the lane to auto-push in your favor and head immediately back into the jungle to hide. Do not give away your position if you don't need to. Do not get overly attached to top. Retake it when your opponents are dead or occupied elsewhere. Don't sit on points thinking you're "defending," unless the enemy is actively trying for that point.
And good luck. Things will be rough at first with bots plaguing low elo and the players there not knowing how to play, but you can climb out of there pretty easily and start getting real games quickly.
