It will be an awesome adventure!
While I personally would lean towards a truck and Travel Trailer either bumper pull or 5th wheel, I echo the comments about getting a motor home instead. Especially if you do not have experience towing. In your cross country journeys you are going to find narrow steep winding 2 lanes with no guardrails, tight spots that require some real skill to get in or out of with a 50' long truck and trailer, high winds going across the plains or in the mountains that make pulling a trailer more stressful, etc.
if you want the ultimate freedom to unhook and go then I'd think more along the lines of the class C for $20-25k and buy a little car to tow behind it for $5k.
Not familiar with the requirements to get licensed and registered to drive it.
If possible since you're going to Vancouver, look for vehcles on the US side of you have a friend to help you with this. Typically the US is cheaper than Canada for the same vehicle or toys.
Good luck with your trip! And have fun!