I had lots of luck with anubias and wendtii when I was first starting out and didn't really know what I was doing (and actually, all I was using was flourite). I have also heard good things about water sprite, though it can be a bit messy. Sword is probably workable as well. I would also highly recommend java fern as an easy, low-tech beginner plant. Flourite red provides some important nutrients, like iron, but swords and crypts may benefit from root tabs.
Yes, the nitrogen cycle will happen on its own and there isn't anything you need to do if you are adding live plants. Adding live plants adds bacteria to the system and provides surface area for it to grow on. Careful adding inverts (snails) to a new tank. They are more sensitive to ammonia and nitrite than hardy fish (e.g. betas).
You don't have any info on lighting. Do some research into this. Getting your lights right will avoid algea headaches. Lights are your gas pedal for algea control. On the topic of algea, you may want to look into using Flourish excel. It has algecidal properties and provides an organic source of carbon for the plants (handle with care). I eventually ween my tanks off the stuff, but I like using it during transitions.