OK, here's my two cents:
It doesn't sound like you're going to be racing this thing, so you're just looking for a bike to get you from point A to point B so you aren't going to need anything super duper light with an expensive set of components on it. With all of that being said I still tend to agree with what some of the other have said about going with a local shop. The Wal-Mart specials are tempting due to price, but as you've said "you get what you pay for". You will probably get a relatively heavy bike with junky parts that will wear out, break, or just not function right. If you go to a local shop they will be able to set you up correctly and service the bike when it needs it. You may even get a free water bottle out of the deal. 
I've always been told, and have found this to be true, to get the best frame you can for the money. No matter how high dollar the parts are they will, eventually, wear out but your frame is "forever". I have a nine year old mountain bike that I have ridden the poop out of and have probably replaced or refurbished every part on, but the frame is still going strong. Many places (shops) have end of the year/ beginning of the year sales and some communities have bike swaps that are a great place to find a great gently used bike. Like the others have said, you really need to sit on the bike because each of them fit different people differently.
At 6'2" you're probably in the ball park with your frame size because other things can always be tweaked to get the bike to fit you better (head sets, seat posts, etc.) The fit calculator that Rickshaw posted is great, but again, this seems like more of a leasure thing for you right now. For a super quick fit check that is actually pretty comfortable have someone hold the front wheel of the bike while you get on it. With the seat set high enough for your knee to be slightly bent when the peddle is at it's lowest point, drop down onto the brake hoods like you where going for a ride. If you look down, the front axle should line up with the cross bar of the handle bars (in other words you shouldn't be able to see the axle). This is usually a pretty comfortable riding position for most people.
As for the bike/frame I would go with steel or aluminum. Steel will be cheaper (probably) and have a more forgiving ride, and aluminum will be lighter but probably jar you a bit more. I would definitely go with triple chain rings in the front. This will give you the option of hitting a "granny gear" on some of the tougher hills and allow you to stay seated while you peddle (most efficient). I run a triple chain ring here in Colorado and I tend to use the smallest ring in the beginning of the season, but as I get stronger I notice that I don't need it as much, but it's always there if I hit an Everest sized hill. The multiple geared bikes (21 speeds) usually have overlapping gears so you don't really get 21 gears (more like 17 or 18?).
The biggest thing, no matter if you get a cheap or expensive bike, is to get a comfortable bike. Like Billy said, if you aren't comfortable on it (it makes your back tweak, or makes your hands go numb) then you WILL NOT ride it. So find one that you like and just get out there and ride.
How was that for long winded?
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