Really depends on what size tank you have.
Mine does not have a cover. I keep the water level a little lower so he can't jump out of my 5 gallon. I do have to add some water mid week due to evaporation.
I tried a snail with Mr. Betta. It did not go well. Now they each have their own tanks.
If you do decide to try an African Dwarf Frog or a snail, you definitely need a cover. The frog will escape and the snail, especially if female, may go on walkabout and risk falling and cracking their shell. Note, I do not have a cover on the snail tank. He's (I'm pretty sure he's a he) has never ventured above the water line so far that I've seen.
Both my tanks have silk flowers, not plastic. The betta tank also has two java ferns stuck in a terra cotta pot with some gravel. He likes to rest in the pot. :D The snail tank has a terracotta pot turned on it's side as a cave.
Someone here posted a link for this nifty tree root looking thingie for decoration which I'll be adding when I've extra $$$$.
Might be a while. :)