Growing up, we always had the little rectangular tank with an air tube and an under-gravel "waste" collection.
Wouldn't recommend that at all.
Two years ago we got a very large tank for our kids (selves, whatever). Went with an external filtration system. LOVE IT. I believe it was about $50 or so, but it is SO much quieter and easier to keep things clean. Even with a small tank, I'd recommend it.
Fish wise? Tiger barbs could be a bit aggressive. Haven't really had a problem with ours. Guppies are great... until they start breeding and fill the tank with themselves. A few were fine, but then the wife felt sorry for all the babies and put 20 of them in another tank. Ugh. Now she wants me to flush a few down the toilet every time I need to do a funeral. Finally solved that with a couple of angel fish which have grown quite large (started out about the size of a round base, now are larger than a coffee mug). They're absolutely hilarious with their piggy-ness. About the only thing I could really recommend is to get fish that are different colors. We had at one time all orange colored fish, and were really disappointed in that. Now have some blue, grey, and other colors so it's much prettier to look at.
EDIT: And re-reading that last line, think about the fish tank as a painting. Pick the colors and highlights you want, and pick the fish appropriately.