I have the following:
Aeropress: Roughly $40 CAD, Quick and easy clean up, Makes a good single serving of expresso.
Moka Pot: They vary in size and cost, but can be found for about $30, makes a good strong cup of coffee.
French Press: Easy to find, about $50 for a decent one, Glass is common, Stainless steel is better, makes also a decent cup of coffee.
Percolator: I have a stovetop one that I bought for camping. Big in size and it's cheap. It makes coffee.
Vietnamese drip thiny: It makes a single serving of very strong coffee. I used this because it was really, really cheap and made a good strong coffee. I stopped using it as the aeropress is better.
I don't have one, but I've enjoyed what is becomming popular these days which is a pourover. There is also a few others (Siphon, True expresso machines), but I don't have much experience with them and some of them are a lot more expensive. They're relatively cheap as well.
If you're mainly making coffee for yourself, I'd look into an aeropress or the pourover. They probably make the best coffee and are both affordable. The aeropress is my daily coffee, because well it's awesome. I often serve the french press as it's bigger or the percolator if I have lots of guests that don't care for "good" coffee.
First thing, find a source of good coffee. You're looking for somewhere that roasts their own coffee and sells it relatively promptly. There are a few online sources as well. (No I wouldn't start at Starbucks or the like...). I don't want to link to places I haven't shopped at, so you'll have to search yourself. Unless you're in Alberta, Canada...
If you really get ambitious you can source green beens online and roast them yourself!
If you can find a burr grinder (not a blade grinder) that would be ideal. You want to grind as close to making the coffee as possible. Coffee starts to "lose" flavour as soon as it is roasted, and even quicker after it's ground. A burr grinder will give you a consistent grind, which means consistent flavour. Coarse grind for french press, fine grind for the aeropress/expresso, medium grind for most of the others.
Now... for the preparation, that varies by whatever machine you use... Check the instructions or google around.
http://www.ineedcoffee.com/: Lots of good information about different brew methods, coffee in general.
http://coffeegeek.com: Really great site with a lot of coffee specific information. At the top there is a Guides & How-To section. If you click that they will have much better laid out guides as to specific preparations.