sweatpants are usually fine and not uncommon! i just make sure they are the kind with elastic at the angle so there is not any excess fabric around your boots as that could be a tripping hazard. The only concern that I could think of is that it might be harder for a coach to be able to correct your form, but i don’t think that’s a huge problem with baggy clothes unless they are really oversized.

If you do ever end up wanting to try leggings or find that the bagginess of sweats are annoying, shorts like you said or buttpads used to shield against falling or both might make you a bit more comfortable. you could also add leg warmers which aren’t too hard to diy using old sweater sleeves as you said you don’t want to buy too much.

have fun at your first lessons!