Hi, welcome to FT.
I know starting with the whole frequent flyer thing seems daunting, but every one of us knew nothing when we started.
If you really want to maximize your earning potential, you should start with the various Blogs that cover this stuff. I'll pitch my own of course (
Onlinetravelreview.com), but you'll learn tons reading
View from the Wing,
One Mile at a Time and
The Points Guy (and others, which you'll discover as you start this process).
It's always good to set a trip goal for yourself, so you feel like you've accomplished something.
You'll want to decide if your credit can handle opening credit cards for the miles. There's a ton of resources on those blogs about this, but in short if you have the credit that allows you to open a few credit cards, you can earn 100,000 American Airlines miles pretty quickly by opening 2 of their credit cards. That'd be a good start. There's a ton of other ways to approach the credit card issue -- once you get those AA cards, people have been very happy with the Chase Sapphire card because it earns double points on Travel purchases, and those points can be transferred to a number of different programs (including United, Continental, Hyatt and more). Plus the signup bonus is 50,000 points. I'm a fan of the Starwood Amex as my everyday card because I like the flexibility of the points transfers to many different airlines.
As for your choice of airline: It's going to depend on how much you're traveling. There's no scenario where I would go with Frontier. Republic announced they were spinning them off, which means they may not be long for this world. Plus, you cannot compete with the benefits of being in Star Alliance.
If you're just making a few trips a year, you may want to fly US Airways and credit the first couple of trips to Aegean Airlines. I know that makes no sense if you're reading about this for the first time, but here's why: Aegean is part of Star Alliance. After only 3,000 miles (well, they give you 1,000 miles for signing up, then you have to fly 3,000 miles) they give you Silver Status, which is good on all Star carriers. So, you'll get free checked bags and early boarding. Better than having to wait til you've flown 25,000 miles on US Airways to earn that.
Once you've hit that threshold, I would credit the US Airways points to US Airways (I was torn about telling you to credit them to Continental, and I suppose that's not a bad option either). I know you say you want to avoid United, but let's be honest -- at worst, it's no worse than any other airline out there. At best, the unlimited upgrades, lie flat seats on Continental's 757s and Economy Plus are pretty good reasons to fly with them. You'll have plenty of flexibility to use those miles later on.
I'm a Starwood guy, so I'm going to suggest staying with them. The annoying thing is that you actually don't earn a ton of points when you stay with them -- you'll really rack up the points thru the Starwood Amex. Part of the reason I suggested crediting the US Airways miles to US Airways (and not Continental) is because Starwood points transfer into US Airways at a 1:1 ratio (while Continental/United is 2:1 - ie, half a mile for every point).
Anyway, that's a starting point. You'll find that folks on the board are happy to answer your questions.