Ghost shrimp can harm bettas, I've witnessed it. Go with red cherry shrimp. They should be cheap and they breed easily, so it won't matter if your betta snacks on them. Yes, acclimate them like you would a fish, they eat leftover food, algae (for the RCS), and microscopic organisms. For a 5g with a betta, you could only get about 3-5 ghost shrimp. You can easily put 10 RCS in that tank along with the betta. I'd say RCS is the way to go. They're fun to watch, colorful, and they are very interesting creatures.
100g Native Fish Pond, 55g Goldfish/Catfish Community, 50g Plant Pond, 40gB Tetra/Cory Community, 20gHM Community, 20gH Turtle (Bender [RES]), 20gL Turtle (Kif [YBS]), 15g Reef, 5.5g Betta (Okami), 5gFBH Betta (Pron), 5gHex Betta (Twister)
2 dogs, 13 cats, 2 turtles, 1 bearded dragon and 1 crested gecko