I have a 2.5gal with a male betta and a oto cat. You could do what some other people said and get a snail but with anything else you are going to a least going to need an airstone because almost nothing else can live without an airstone and/or filter. Filters cost about $10 for a whisper for a 10gal. Yes, you can use a 10gal filter on a 2.5gal tank. The betta will get use to the current. It's better the getting sponge filter, in my opinion, that works not as well and cost more or the same. Do you have a heater? If not you can get one small enough for your tank for about $6 at walmart. The air pump is around $6 as well. The airstone is a $1 and the air-line tubing 89 cents. So if you really what to be able to keep something else in your tank you can get those things and spend about $24, misnus the fish.
Sea-Monkeys. hahaha. My english teacher had a little container of ''sea-monkeys'' on top of his over head by the window. I was half tempted to go up to him and say ''so what are you feeding with that brine shrimp hatchery over there'' He'd be like ''what?'' I don't think he know anything about fish, not to mention what ''brine shrimp'' are. hahaha!