Ugh, carpet plants are very difficult without co2. I know, I've tried! I would say you best bets might be HM (same genus as dwarf baby tears, HC; sometimes called MM or just baby tears, be careful! They're hard to tell apart!) but it can want to grow tall rather than a carpet. It'll need trimming & replanting to encourage it. Monty Carlo is similar to HC but a bit easier to grow...for some...
Dwarf hair grass is hard! It doesn't spread densely & is prone to a few algae. Skip it. Difficult, but pretty to me is cryptocoryne parva. It's slow growing & slow spreading but I love crypts & may try it a few more times
Glossostigma or staurogyne might be worth a try. I've grown them well...for a while.
If you just want some low growing plants without an actual carpet effect I'd suggest dwarf chain swords (Lilaeopsis). I have New Zealand (but in latin, it's novae zealandiea (?). It spreads but in a long chain, hence the common name. You can encourage it by pinching or snipping the plantlets & replanting.
After 40+ years, I've never tried a dirt tank, they come with issues of their own, think hard before that's your 1st tank. You need to get a grip on the basics & try easier plants first.
I do have to say I'm not the most consistent fertilizer & prefer root tabs that last for 3-4 months rather than dosing every week. It can be hard to find a good balanced fertilizer, liquid or dry. To me it's kind of a math test but with your water parameters too.
So, what size will your first tank be? I will suggest a 20g long tank. It's shallow enough to help with lighting but big enough for some fish & plant choices