Live plants or not?

Live plants are only a lot of work if you make them a lot of work. Also, I just put a whole slice of cucumber at the bottom of my tank and the betta can't get at it

 

There really are no upper level fish suitable for a male Betta so it would be best to leave him on his own. Invertebrates are fine.

As for plants, like all anabantids the Betta "expects" floating vegetation so some simple floating plants would provide this along with the water quality benefits. Water Sprite is ideal, but Water Lettuce and Frogbit also work. Some of the stem plants do well left floating, such as Wisteria and Pennywort. Provided your light is suitable nothing can be much simpler than floating plants.

 

I would suggest some anacharis. It is super easy to grow, fish love it, and it grows really high, so it will reach the top of the water where it will then bend over and grow on the water's surface. This is actually kind of a win-win because you will not only have a plant in the gravel for your fish to swim through, but the top will float on the water too.

Another great plant for bettas is a marimo moss ball. They require almost no care, and look really cool. Bettas really love to play with them, and rest on them too. The moss balls are also really good for your water.