There are lots of possibilities for inverts, as OG said.
For corals, you would do best with the easiest varieties, since you are just starting out. Mushrooms (corallimorpharians) and "polyps" (zoanthids) are quite hardy, and won't outgrow a small tank. Star polyps, a group of mat-forming soft coral, will also be good. They are usually inexpensive, as corals go, and online vendors often have "nano packs" of hardy corals.
Peppermint shrimp are also easy to care for, and can be had for $6-$10, depending on the source. Skunk cleaner shrimp are more attractive and outgoing, but can be about 2-3 times as expensive. A pair of either will work in a nano of reasonable size. Hermit crabs can be very interesting, and make good cleaners, but get non-aggressive species like scarlet reef hermits. Small snail species, like ceriths and nerites are good for algae control, as well as slightly larger species, such as Astraeas. Turbos and trochus will get too big.
Fish? My preference is to avoid fish in any tank smaller than 10 gallons, but small species like neon or clown gobies will do allright.
I would depend mostly on the live rock/sand for filtration. Lighting will depend on the corals you want to keep.