Your question would probably be better answered at Plantgeek, or in the plants forum. Information that would be helpful: What type of lighting are you willing to provide? Substrate? Ferts? etc.
If you aren't willing to pour your funds into specialized plant care products (which tends to be quite a bit more expensive than than the fish or the plants themselves), then your best bet is simply to research low light plants, as the bettas themselves don't actually care what plants are in their tanks, so long as they can rest their royal rear ends on them when they feel a nap coming on.
My singular warning: I witnessed one of the sharper hornwarts actually tear a male betta's fins as he sat on it, one time. While this particular betta might have been more delicate than others, you have to admit, your standard issue VT is a delicate sort when compared to their hardier breeder/wild caught cousins.
My male VT tends to favor the java fern and anubias plants, which in my 5g are large enough to be an inch away from the surface of the water. He sits on them and sips the oxygen as he sees fit.
Planted 5g tanks or less have a lot of problems, fair warning. It's worth the effort if your goal is to provide your betta with the "kicken-est crib in town", or if you have a yen for aquatic bonsai, but if you aren't willing to spend a slap-silly amount of time and money on it, your best bet is fake plants (he won't know the difference. >< )