I would suggest at minimum a 4 person tent. A 2 person tent will get very old very quick.
I totally understand shopping on a budget, which totally limits your options.
Even with that said, try to find the tallest tent that you can. You will get sick of having to change your pants laying down very very fast!
I'm not sure if I can post a recommendation for a certain tent by a certain manufacturer. So Mods, if this is out of place please feel free to delete it.
My sister has this tent. It has A LOT of mesh around the top, but with a few spring clamps something like these

then you can attach a sheet pretty easy. This tent is large enough to fit a queen size air mattress and a suitcase or (2) 'rubber maid' storage contains in. Just make sure that if you use an air mattress that you inflate it inside the tent, cause it wont fit through the door when inflated.
http://www.amazon.com/Coleman-Sundome-4 ... +sundome+4
Our first year, a camp mate used this tent. He really liked that it had a little "awning" type deal, which if you put a small tarp under, it makes a really good place to take off shoes and really dusty clothes before you get into the main tent area. It also gives you a lil privacy to get undressed out side of your tent, so that you don't track a ton of dirt in.
http://www.amazon.com/Coleman-200000159 ... eason+tent
This is an Amazon search for "4 person 3 season tent" then I refined the search to 50-100 dollars. I think in the price range that your looking, you're going to have a lot of trouble finding something that doesn't have a lot of mesh.
http://www.amazon.com/s/ref=nb_sb_noss? ... =386589011
We're going through the same thing right now trying to find something for the 2 of us, that is under $250. We're gonna be on Playa for 11 days, so we need to up our game a little. I can't do another week or longer of having to change my close laying down, and hunching around in the tent. Just having to hunch in the tent ends up killing my lower back after a few days.