Anything, even an economy sized car, should work. Worse case scenario, the trunk is tiny, you put the 2 backpacks in the trunk and the suitcase on the floor of the car. The 2 year old shouldn't need much legroom.
Unless your suitcase is huge you should be able to put the suitcase and at least one (and probably both) backpacks in the trunk.
An economy car might be two door model. Compact car could be a 2 door, I think 4 door is typical. I don't know if that's an issue with car seats.