If you have trouble finding an affordable short queen, go with a full. It’s the same length, only the width is 6” shorter, so it’s pretty close. My trailer came with a fold up Murphy bed mattress, and it sucks bigtime. Had to replace it after about six months. If you’re concerned about weight, avoid memory foam. It’s heavy and more expensive than a spring mattress. Walmart.com has a full spring mattress that fairly affordable. Also look into second hand furniture stores nearby. You might get lucky and find something under $50.
