I like Anacharis (Elodea) and Amazon Sword plants. The anacharis can grow floating or anchored, is very tough, and absorbs lots of waste and ammonia/nitrates. Amazon Sword is also tough and hardy, and the large leaves provide nice "Betta hammock" type places for the fish to rest on. Thick clumps of anacharis make good hiding places, too.
Personally, plants scare the pants off of me!
It was because of live plants that I lost my Persica. :( They started dying, contaminated the water, and as a result he got a bacterial infection and passed away... It was very traumatic.
So I stick to the fake.
I really like soft silk plants from Petsmart.
That is why I stick to hardy plants, and remove any dead plant matter when I come upon it. :) But everyone has different preferences. I've seen more Bettas injured by fake plants that anything, hence my general dislike of them, but if they are soft enough, they're great.
I've got some Argentine swords, pennywort, wisteria, a banana plant, and marimo moss balls, as well as some plants I need to replace with true aquatic. Be careful of what's listed as aquatic at the pet stores, they label terrarium plants as aquatic plants.