So my winter beater bike needs a new chain, as it's started skipping lately anyway. My grandma always gets me a $20 x-mart gift card. I don't normally shop there, but one thing I think they do carry that I need is a new chain. Would one of their cheapo chains be suitable enough for beater bike duty?

You should be able to get a cheap chain for under $15 from a LBS or x-mart and it will work just fine. However, once it starts skipping you may well need a new cassette (or freewheel) as well.

I was reading about that. I didn't really see much on how to tell if the cassette is done for, though. How can you check it?

Though I think mine is due to binding links due to winter and not being lubed properly heading into the poor weather season.

Put a new chain on and pedal around a bit is how I check it. I would assume you could see how much your current chain is stretched and make a guess though.

people will say the driving edge look like a hook or something , but I've had to replace 2 cassettes and neither one looked bad to me, or in one case the bike mechanic, but the new chain sure didn't agree with them.

edit: my opinion is a chain is a chain unless you're a weight dork or something.

Make sure the width is correct for your drivetrain. In essence, if you have an 8spd cassette, get a 7/8spd chain (they're the same). If you're running 9spd out back, you need a 9spd chain.