Cory's will only eat algae if they are starving and its the only source of food. Dont rely on them to eat algae.
Live plants is the only way to go in my opinion. Betta and cory will not eat your plants but some snails will.
I found out that if theres enough stuff to look at in your tank, your betta will be too occupied and curious to give a crap about other fish. My betta is always trying to fit herself between plant stems and some of my Anacharis and she likes squeezing herself into my Japonica.
Also, Cory's are pretty sensitive if not acclimated correctly. Im not going by what I read, im going by experience. Do it slow. I literally take 2 hours to acclimate my fish and even longer for my shrimp.
A good snail to get once your take is established is a nerite. Theyre really good looking, dont reproduce. Theyll lay eggs but they'll never hatch unless in brackish water.
From what i've learned and from personal experience, all fish like a real environment. Driftwood for sucker fish because its what they really suck on in the wild and my cory's love "sniffing" this thing, and live plants for natural cover and oxygen. Bettas really are super hardy animals and can live in some crazy tanks and less than perfect conditions but other fish do a lot better under more of a live surrounding.