Clipless Pedal Help

Don't know if you're after road or MTB pedals but if you stick with the reputable names like Shimano, Look, Crank Bros, Time etc you should be fine.
Installing pedals is quite simple. Get yourself a pedal wrench. Most pedals are installed with one of these. Some use an allen key and others have both (eg Crank Bros). The pedals will indicate whether they are left or right; usually found on the pedal spindle. Make sure you install the pedals on the correct crankarm otherwise you could strip the thread.
In short, yes there is a difference between $100 shoes and $300 ones; build quality, features (eg velcro strap vs click lock systems) , material (carbon sole vs compsite soles) etc. Again, depending on whether you are after road style or MTB there are some decent models from the likes of Shimano which are suitable for those new to clipless pedal systems. Try them on as the sizing between brands can be a little different. Also if you have a wide foot some brands and models might not suit you. Best to go to your lbs and ask to have a look at their range.

Are $300 shoes better? Yep.
Are they worth it to you? Depends on how much money you have, but probably not yet: they are stiffer, fit better, last longer. I wouldn't commit that kind of money till you have some experience with clipless: start with a snug but comfortable all purpose shoe, and when you've worn that out, you'll know a lot more about what sort of upper end model will suit you-- there are a lot of variables.

As to clipless systems, I like crank bros. because there's a wide range of compatible pedals [mtb, race, cruise, etc], and the cleats for the shoe are small and thin enough that you can walk almost normally.

But there are a lot of valid choices-- there is more than one right answer to this question.

I'm a big beleiver in supporting your local bike shop, especially since they can give you some guidance as to finding a shoe that fits both your foot and your riding level. Very important if you feet tend to be between sizes, wide, or otherwise hard to fit [do you know your metric size?]. But since my nearest bike shop is 80+ miles away, I often turn to ebay and the bigger online bike stores: Performancebike.com and nashbar.com . Sometimes sierratradingpost.com have some good buys, too.

This is a good time of year to be shoe and pedal shopping: big discounts out there as fall approaches.