Coral is absolutely possible! In fact that's probably where you'll focus much of your effort. While a smaller reef can be more difficult to stabilize, it is much much more affordable. 3 fish may be pushing it, but I could see a clown goby, and watchman goby. You may even be able to put a royal gramma or firefish in that mix also.
Because its a smaller tank you save a lot of money on rock and filtration. There's really no need for you to have a protein skimmer. You can get 20lbs of live rock for like $100, and one circulation pump that moves water about 1200 gph
. This may seem like a lot, but it's not. Theres no need for you to have a HOB
filter or anything like that, because the circulation pump filters the water through the live rock. You could pick up a Ehime Surface Skimmer to remove the surface slime though.
I'd highly recommend ATO for a smaller tank unless you plan on sleeping next to your freshwater for evaporation top off. I recommend the Tunzee Nano ATO if you're looking to save some cash. Depending on type of light you get dictates corals really. I'd consider a Kessil A150 for this tank.
So you're pretty much fully set up under $500.