There are many awesome invertebrates you can consider adding to the tank. Some will eat others so it is best to know what you would like and then see if it fits with the rest.
You can find a previously owned tank, cube, but you can do a reasonable cost small tank. Let me warn you as someone who thought that it would be not too hard to do a small tank on the bargain side of things, there are too many really awesome things you will end up wanting.
As for the size of a tank you might want to get a little arger, Petco has dollar per gallon sales maybe still on now and many companies sell inexpensive kits with a lid and light for freshwater and if you don't want coral right away just fish you have a couple considerations.
One is a 10 gallon tank doesn't really hold much for fish, maybe 1-2 fish like one clown fish and one Clown Goby.
You can do a much larger, say 40G breeder size (3' wide) and have a few fish with a light with some shrimp and crabs and different types of snails and an Urchin which was one of my favorites.
Check out this POTM winning 40G tank.
Anyway if you are set on a small tank start reading through some of the builds with small tanks and start learning from everyone and that might help you decide whether you want corals and will be willing to take care of their needs. Or fish and what kind you might want because that will also help you decide on what size tank you are going to need. If you want a Tang your gonna need a 125G minimum, lol!
A 15G tall would be good if you just wanted a Clown Fish (Ocellaris or Purcula, not a Clarkii or Maroon) and Clown Goby Green or Citrinis or Yellow.