I got it! I thought you mean "natural planted tank" which is, IMO, more work that sand substrate.
It's mostly stem plants like Wisteria, Cabomba, Anacharis, Hornwort that can grow out of control.
Anubias are great, slow-growing plants which don't need to be planted but can either be floated or tied to driftwood or ornaments. Anubias do fine without fertilizer ... at least mine always have because I'm very forgetful.
... and they definitely prefer low light.
Cryptocoryne are easy and don't overtake a tank. They do need to be planted and need the addition of root tabs. The one downside with Crypts is they sometimes "melt" (die back) when first introduced into a tank but they usually come back just fine.
Or, there is a really nice plant, Red Tiger Lotus, than can be a focal point. You can let the pads grow to the surface. Or, you can decide how tall you want them and clip the stems back when they reach that height. Eventually they take the hint and won't grow any taller but will become nice and full.
What a task you've taken on Mom, Spouse, Student! Not sure I ever had that much energy.