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I've been looking over the rules and I like the models but I haven't been able to find a good description of what each faction does playstyle-wise. Can anyone give me a short overview of each?

I'm on my phone, so I'll give you the short version.
In Infinity, the factions aren't so different from each other playstyle-wise. Every faction can do everything. However, there are some things that sort of set the factions apart.
PanO is solid units, good all around and very cost efficient. Many different TAGs.
Yu Jing has lots of Heavy Infantry and some very good close combat units.
Ariadna guys are low-tech and cheap to field.
Nomads rely on playing dirty.
Haqqislam have lots of light infantry, doctors and some exotic weaponry.
Aleph is a high-tech elite force.
Combined army is a specialist alien elite force.
Tohaa is a synergetic alien army with units working in groups.

But the reason it's hard to find a rundown of what the armies do is because it's really different from other games. In 40k, Tyranids are a swarm, Necrons are resilient, Space Marines are elite, Eldar are mobile and agile... in Infinity the difference is not so big. Any army can field an elite force, or a mobile force, or a sneaky force... and for that reason, the general advice given is to make your choice of faction based on how they look.

Not to be rude, but try a search next time. A thread about this was not many threads below this one.
http://www.dakkadakka.com/dakkaforum/posts/list/626913.page

Hope this helps and welcome to Infinity.

^ That basically. There are a lot of requests for that (including myself a while back if I recall correctly). It may be more helpful if you do a little research and decided what kinds of things you want to do or what army appeals to you from a visual/background perspective, then we can all give some better advise on how to proceed.

I came in with a vague idea of wanting to play an army with all the dirty tricks and control abilities, and fell in love with Combined Army because of...pretty much everything really.

Thank you for all the suggestions and the links; on model appearance I'm thinking PanO's in the lead but I'm going to do more reading before making a final decision.