Among the small snails there are Malaysian Trumpet Snails (MTS) and common pond snails which will leave healthy plants alone, eating only algae and decaying plant matter. Some think of these as pests and once introduced into a tank, can be nearly impossible to get rid of.
You could also consider Apple Snails (Pomacea bridgesii) which will leave healthy plants alone, munch on algae, and whose population is easily controlled.
I don't consider apple snails efficient algae eaters. I would go for olive nerites, they are exceptional algae eaters, don't harm plants, don't reproduce in freshwater (although they will lay eggs), and are easily supplemented when the algae is gone.
I can honestly say I think they would be just fine. They have very fine antennae and not alot of exposed "body" so I don't think bettas would bother them. My "killer" betta is kept with about 4 nerites and has never had an issue although he kills every other invert placed in his tank.
I know what you mean about killing every other invert in the tank. My bettas killed two cherry shrimp I couldn't catch to transfer to my 10g, as well as most of the small ramshorn and pond snails that where in the tank.
I'd like to try some. How many do you recommend for an Eclipse 6 system (5.5 gallons) that houses two bettas (1m, 1f) and two neons?
i wouldn't put more than 1, you would be amazed at how adept they are at eating algae. Do you have another tank you could move it to just in case the bettas want some escargot? I really think it would be ok, but you should always have a back up plan especially if you know your fish is agressive.