i inherited one from a mate who moved to tokyo. woudl like a bigger one really but space at my girlfirend's is limited.
firstly, i'd stay away from goldfish if i was you... they're messy and grow too big.. they're pond fish really.

get yourself a good filter (essential) and probably a heater too (as most houses aren't warm enough to keep the water temp high enough for tropicals).
i've got a common pleco (shouldn't really have him as he'll get too big for the tank hbut he keeps the algae down!), a guppy, a couple of glass catfish, a dwarf guarami, giant danio, 3 black widow tetras, a couple of cardinal tetra and some white cloud mountain minnows.
all pretty peaceful fish and get on with each other ok, unlike the figure8 puffer fish i had who whilst very cute and interesting was extremely agressive and attacked the others constantly. (i've since found out that keeping puffers with other types of fish is usually a bad idea!)
really not hard to look after... i just do a 25% water change every week or so and test the water quality regularly to make sure it's not got too much pollutants in it.
other than that, most important thing is probably not to overfeed them, and to buy your fish based on compatibility with existing tankmates and also bearing in mind the size they will reach when adult!

there's loads of good info on the net... try fishkeeper.co.uk or practicalfishkeeping.co.uk