well.. i can tell you from experience that ghost shrimp aren't poisonous. and usually if there's plenty of room (10gal is plenty), there should be no problem with shrimpicide. ghosties have a bioload of near zero (meaning their waste is at the zero end of minimal, so you can have quite a few), and they will eat their own shell after molting. speaking of which, make sure they have a few hiding places when they do molt.. they will be vulnerable for a few days afterwards, and your betta may take the opportunity for a nice snack. they don't eat poop
but they will love any leftover pellets or flakes that fall to the bottom, and they will feast on most types of algae (not the stringy kind or the black stuff, just the blue/green and brown fuzzy stuff).
Elvis had a few ghosties in his tank for a while.. until one made the mistake of trying to groom him while he was sleeping. i found pieces scattered everywhere the next morning. Simon currently has a Japanese Algae Eater (Amano) in his tank, and so far they're buddies (there were two, but one died day one due to petco being jerks and dropping him on the floor).
basically any kind of freshwater shrimp are ok, so long as they match the temperature requirements of the betta (there are a few that don't, but they're expensive and i can't remember their names). ghosts, cherries, bamboo, amanos, tigers, jades.. i'd say start off with ghost shrimp. they're the cheapest, and if your betta kills 'em off, you're not out a small fortune.
the best way to describe shrimp: they're like roaches. they move fast and jump even faster. when moving them from tank to tank or bag to tank, keep your hand over the net until they're in the water. when they're in the tank, keep it covered. yep, you may find 'em in your filter now and then, depending on what kind of setup you have (i have marineland hex 5's, the setup is on top and well above the waterline, but that didn't stop my bamboo shrimp from swimming upflow and cramming his chubby carapice in there). ghosties are an especially irritating pain in the arse, because unless they're egg-heavy, you can't see 'em when they hit the floor. to be honest, though, i've never seen a ghostie in the filter.. they usually cruise along the bottom in a herd.
that's about all i can think of offhand.. lemme know if i missed anything.