You probably want something roomy, definitely reliable, and cheap to operate (good gas mileage). You also need something I would characterize as very affordable. It's going to be hard to find all of these things in one car...but we can try.
- A 2012-2014 Ford Focus 5-door (aka hatchback) is a decent new(er) option. The rear seats fold down, reliability is good so long as you avoid the fancy electronic systems, and they're available for around $10k with less than 50k miles if you look. It's not a "big" car, but it will work.
- Nice used sub-compacts like the Yaris, Versa, Fit, Rio, etc. are available all day long for $10k (often still under factory warranty), but these cars don't have a lot of room. You might have to leave your jokes at home if you go with a car this size.
- If you're willing to drive something older with miles, you can't really go wrong with a Toyota Camry or Honda Accord. A Subaru Outback wagon might be a good option too - they've got lots of room for your stuff, and AWD too. But you'll be spending $10k on a car with 100k miles, which can be hard to do for a variety of reasons (sometimes, lenders won't let you borrow this much on a high mileage car and/or they'll set a 36 month limit on your installment agreement).
Good luck!