Certainly a loaded question! The fish you should get totally depends on your tank, level of free-time, water parameters (water hardness and pH are the ones most referenced here, as they're typically unchanging figures that can make or break the peace in an aquarium), your wants, e.c.t.
For a tank that could fit on a table or desk, you're looking at maybe 5-15 gallons? Of course that depends on the table size (and sturdiness). Many people suggest bettas (or Siamese fighting fish, as some still call them) for smaller tanks. They're a solitary, generally calm fish that don't mind living in a smaller space. Most recommend at least a 5 gallon tank, but bigger is always better! While aggressive towards their own species and others, they can usually be seen housed with shrimp such as cherry shrimp. Vibrant, attractive, small shrimp that add a lot to a small space. Easy to build a colony of them too, if you're planning on taking over the world with them. Both cherry shrimp and bettas prefer a more neutral pH, and softer water.
For bigger tanks (20+ gallons), the possibilities are almost endless. In my 230L (~60 gallons), I keep three species of plec, tetras, fan shrimp and more. It's around 4ft, and provides more than enough space for my young fish that are all within the 6 months to 1 year old age range. Take a look at some of the tanks owned by people on the forum. You can find "journals" of tanks, including many photos from forum users and how they get their aquariums to where they are. Lots of folks have links to pics of their tanks in their signature, such as
@WhistlingBadger and his setups.
Here's a full thread by
@Slaphppy7 showing off all his fancy thingamajigs.
