Most fish 6 inches will be able to eat neon tetras. (most cichlids, catfish, and cyprinids get large mouths) Gouramis are nice and colourful, I like the gold, 3 spot (blue), pearl and snakeskin gouramis.
*Some gourami are aggressive towards other gourami so it is wise to have only one or to have several to distribute the wrath of the dominant male.*
These fish grow about 5 inches long.
Glass catfish are really cool too. They need to be in large numbers or else they die. Go for as many as the LFS has in stock and then go again and buy their entire stock again. You should try for 6 or as many as you can get. There are 2 distinct kinds: ghost glass catfish and the 3 striped glass catfish. Both are awesomosaurus. If you end up with a low number (less than 3) you still have a few months to get more before they die of stress.
You will want many more neon tetras. Some people aim for like 20-30 or so. consider 8 a good number to start.
Having fish as small as neon tetras make it difficult to stock a large tank such as a 80 gallon. Filament barbs get to 6 inches and rosy barbs get to about 4. Both have really tiny mouths. Spanner/T barb might get large enough to eat neons or shrimps. Contrary to popular belief barbs are very peaceful in numbers greater than 4... with tiger barbs this number must be more than 10 to ensure safety.
The red tail black shark (or other red and black "sharks") get to about 6 inches and are semi peaceful .. but intolerant of other similar looking fishes.
Some good tetras to try (in numbers over 6 please) are congo tetra, flame tetra, black neon tetra, black widow or black skirt tetra, lemon tetra, head and tail light tetra.
The dojo / weather loaches get to like 8 inches and have tiny mouths... tiny eyes... and are thin like eels.
Try the "good (and bad) beginner fish" thread at the bottom. It will be extraordinarily helpful.
http://www.monsterfishkeepers.com/forums/showthread.php?t=21847