In terms of size? Two sizes larger than you think you need.
I would ask the people you are renting it from what they recommend. Be clear what your house is like - It's a 3 bedroom with minimalist living, though we do have 5 kids. Or it's a 4 bedroom with some mild packratishness. They'll be able to steer you in the right direction.
I'm moving, too. BF and I bought a 20 ft with 4 ft v-nose enclosed car hauler. I figured I could get practically my whole house in there. Boy, was I wrong! I've hired movers with their biggest truck to take the majority of the house. After we get the trailer unpacked, we'll go back to the house to get the rest of the things, which hopefully won't be much.