You asked - "What in-expensive router would you recommend to replace the current one?"
I am loath to recommend a specific router. Mainly because I'd only go with my personal experience and since we don't live together what works best for me might not for you. And while I'm sure you understand that and would keep it in mind, I still don't like getting into specifics. Honestly, any of the major brands; Belkin, D-Link, Linksys, are going to make great products. TP-Link seems to make a good product as well. A few years ago I'd have said Linksys and never looked back but something happened; not sure if it was because Cisco bought them or not but their routers turned to crap or at least the ones I have been exposed to.
My recommendation would be rather than buy online, buy from Wally World they sell all the major brands. You can take it home hook it up and just test the range. If you get enough range then keep it or you could spend a little money and buy like 3 of them take the ones back that don't perform the best. I say Wally World over online ONLY because returning it is hassle free with a receipt.
If you find you get the coverage you need, happy days. If not no worries, setting up the repeater is a breeze. there's steps but they aren't hard to follow. But first the new router.