It's almost certain to be English threaded, so there's your bottom-bracket-to-frame interface. The other thing you'll need to know is the spindle length, which is determined by your crankset. You'll likely have to remove both crank arms and measure.

...but a decent threadless bottom bracket that doesn't require chamfering the bottom bracket shell will probably cost you around $60. (The Velo Orange Grand Cru threadless bottom bracket would be a safe choice.) Add labor and/or tools and you're quickly spending more on the repair than you did on the bike.

There are cheap threadless bottom brackets out there like the ones by Sunlite or YST, but you're supposed to chamfer the edge of the bottom bracket shell to get those seated properly.

If you want to attempt a low cost fix, you might consider trying a heavy duty retaining compound like Loctite 609 to secure the stripped cup in place. Especially if it's the fixed cup (same side as the chainring) since you won't have to remove that one to adjust or service the bottom bracket. Will it hold? I don't know. But at least you're not throwing money at a bike that may not be worth high repair costs.