Snails (Apple snails aka Gold/Blue/Black/Ivory mystery snails) do keep down the algae and they also eat the fish poopie...however, keep in mind that since they are eating they are pooping too. it can look untidy when you got snail turds on your glass but ultimately their by product hasnt been a hassle. it falls off the glass soon. i have a gold snail and blue snail and also a teeny baby snail that stowed away on a plant i brought home in a 10 gal tank and my bettas dont mess with em. only thing is you may have a betta that will take a bite @ their antennae so just keep a look out. id advise getting just one, no more than two.. start with one and see how you like it. im not positive how much they eat but two snails to one fish sounds like competition for food but they can also be fed algea wafers (the ones you give to those sucky algae fish), they go nuts on those. FYI snails are awesome to watch...they do some pretty cool stuff under water.
Apple snails are less effective for an algae eater compared to nerites. If you want a snail, keep 1-2 nerites only but do supplement them with extra algae afterwards since they will not eat commercial foods unless you are lucky yours of hundred nerites will eat a pellet enthusiastically which rarely happens. The other option is pea-flavored snail jello.
I will not recommend apple snails with bettas. Bettas are very poor tankmates for snails to be honest. They prefer soft water as hard water required for these snails will increase their chances of suffering finrot and other bacterial infections.