I am a fishaholic. If you have any questions FX-7 feel free to ask.
I currently have a 33 gallon fresh water tank that houses:
1 Black Ghost (Possibley the most exotic fresh water fish I've seen, imo)
1 Bubble Eye (Just plain wacky)
1 Pleco (As Chris said, bottom feeders are great for cleaning, plus they are a pretty cool looking fish
1 Dwarf Frog (Don't do like me and let your wife buy him and put him in a tank with a Ghost or Gold fish, he is a target at all times)
My tips to someone new:
Start small, one or 2 fish maximum.
Try to get a tank at least 20 galoons or more. A bigger tank stays cleaner and healthier, while allowing the fish more room to swim and be "fish".
Do not over feed the fish. 2-3 times a day in small amounts. Most fish won't stop eating untill it runs out. Very important.
Don't buy fish from a store that has a dead fish in the tank, or even worse, multiple dead fish.
When buying, stare at the fish you are interested in and make sure he does not have any white dots on him (looks like salt), if he does he has ich. A very common fish disease. Can be treated but it's a real pain. Also look out for aggressive fish, trust me you don't want those.
Becareful what fish you put together. For example put more then 2 Angels in an average size tank, and watch them get extreamely aggressive.
Do not buy standard Goldfish or Koi. They will outgrow any tank, are filthy and cause stress (stress allows for disease and eventual death) to other fish. They are suited more for a pond, contrary to what the pet store says, they just want your money.
Clean the tank at least once a every two weeks. Change all the filter medium once every 1-2 months and use a water conditioner to neutralize the chlorine in the water.
This is the bare minimum you need to start:
20 Gallon tank: $50-$100
Water Heater: $15-$40
Power Filter: $25-$50
Plants and Rocks: $20-$30
Chlorine Remover $5-$10
Fish $1-$25 (although you could spend hundreds)
Cycle: $5 (helps get the tank ready with helpful bacteria)
I just recommend doing your homework as it is quite an investment in time and money.
Recommended fish that aren't too expensive and are pretty easy to care for, yet look awesome:
Black Moor; while mid to full size can cost up to $35, small young ones can be had for under $8. A mezmerizing fish. All black, and huge, with personality.
Angel: Great fish, but does best when he's the only Angel. $5 for a baby, up to $40 for a very large one.
Plecotomus: The perfect fish in my opinion. Under $10 for a young one. Gets very large.
Rainbow shark: One of my favorites. Not really recommend though. Just damn cool. Do not put with a pleco or other bottom feeders in a small tank.
There is tons more info and tons more fish. Take your time and do some reserch. It is very rewarding if you stick with it.
I'll stop now.