Which plants for my 3.5 tank?

I've used this forum forever finding advice for my betta. Now comes the time where I need advice and can't find it so I finally made an account.

A year and a half ago I bought a bright red half moon betta the same time my friend did. We both listened to the petstore worker who said betta's were perfectly fine in a bowl and water changes just needed to be done once a month.
I figured that was an error because my friends fish died a few months in. So I starting building up. I started by getting a bigger bowl, than a bigger one. Gradually building up to a 3.5 filtered roofed LED lit tank with oxygen stone bubble blower.
My fish has seen his share in tanks.
Now I still want to build up. My fish is far from a truly optimal tank. He still needs a heater and thermometer (Which I'm getting soon) and I know he needs live plants because the plastic ones just scratched his fins :-(
So my questions are:
What types of plants will be good for my 3.5 betta fish tank?
Can LED's offer any good light for the plants?
I have an algae build up problem so will a Nerite Snail work in this tank?
Will a Netrite snail eat any live plants if I put one in?
Netrite snails and bettas are compatible right? Apparently they are but playing it safe and looking for a second opinion.
Are there any diseases or sicknesses a plant or snail could infect my betta with?
How would I introduce any plants into this tank?
Usually (I read) you by the tank and the plants and let it go through a full cycle to help grow healthy algae.
But I already have Marvin so should I (if I do) put him in bowl again until the cycle is complete and the tank is ready?
Or do I just put the plants in during a water change, let it cycle a bit and than put Marvin back in after a shorter period of time?
I really don't want to put him into shock, what effect could the plants have on him? (probably none but still, playing it safe)

Finally If I were to get the plants and the snail and it runs smoothly would water changes become more frequent because the snails excrement or the same amount of water changes because the plants balance off the ammonia level a bit?