Your options will be limited to the species allowed and provided by your Fish and Game division/department. When you stock a private water body, you need a permit from your state government, and your Fish and Game department will provide the fish to be stocked from a hatchery. This process is not like going to the deli -- you can't say, "Give me a bluegill, a couple crappies, and a nice big bass." They will tell you if you can stock fish and what kind of fish you can stock, based on characteristics of the pond, its connection to other waterways, etc. Since this pond is fed by a small stream that means its hydro logically connected to other waterways and the state will want to be careful about what they put in there. Usually nonnative species are not stocked unless they are sterile, which means you have to restock periodically.
If you're not doing this the "official" way, then you're sort of rolling the dice. A lot of unexpected things can happen you embark on a career as an amateur fisheries biologist. Let's say you decide you want bluegill in your pond. You go to some nearby lake and catch a bucket of bluegill, and then you bring them back to your pond. Who knows if they'll survive? Maybe the pH is off or the average temperature is too warm or there's not enough biomass to support fish. They may all die off or they may migrate away through the stream. But let's also say that a few carp larvae got sucked into your bucket of bluegill -- within a few years your pond will be full of carp, and then it won't be fit for anything.
But let's forget about the problems of amateur fish stocking. I'd say that your pond is probably best suited for crappie or perch, which have a high tolerance for temperature variation, can spawn in lots of habitat, and can survive on a wide variety of forage (including each other). They're also good to eat and fun to catch. Here again, however, you run into problems if you just start throwing fish into a pond. The most common problem with sunfish I've seen in small lakes and ponds is overpopulation -- sunfish will fill every ecological nook and cranny and soon you will have an abundance of fish, but only a small percentage will be big enough to fish for.