Just a heads up, both shrimp nor snails will clean your tank, every living thing producing some form of waste. While some species of shrimp and snails do clean algae, they need to eat more than that and will produce waste.
You can definitely keep shrimp or snails in your tank, but I don't recommend adding shrimp right off the bat, they are susceptible to fluctuations in water parameters, which can easily kill them. It's best to allow your tank to mature for a month or more to achieve a stable environment.
I personally would suggest a nerite snail for your tank size, mystery snails can get larger and produce a lot more waste, the nerite is also a better algae eater.
I have kept snails with my bettas, they did just fine, but eventually, my water became a problem since softeners used beyond my limit of control, and they died due to the unstable GH/KH.
They won't have any issues eating off of the plants, snails weigh very little, and they can find their way to eat algae as they favor.
Shrimp may be eaten by your betta, but that also depends on whether your betta has enough interest to hunt them, or if your shrimp are brightly colored.
They do breed, and if your betta wants to eat them, you may have the best success with providing places for the shrimp to hide, and the shrimplets could be eaten by your betta.
My shrimp bred a couple generations, and the offspring were kept in control by the betta, who slowly ate them over a long stretch of time.
would have some good suggestions on this topic as well.