If you're worried about recurring your Torments, you're better off with Eternal Witness, it gives you a decent body and can get back anything you need.
I'm not going to lie, modern is far from a budget format, the only moderatly inexpensive competitive deck I've seen is mono-red burn and even that sometimes uses fetchlands just to thin out the deck of lands, I'm sure the deck will be fun to play but at a PTQ you're likely to face people who can deal infinite damage/gain infinite life on T3 and other shenanigans like that, regardless it will be a fun experience but I'd suggest testing on Cockatrice first just so you have an idea of what's coming, I usually title mine "Modern Homebrew" when I'm playing a deck based on a combo.
Just my 2 cents, I hope I didn't sound mean or depressing I do think you'll have a great time either way!