A motorhome for $2,000 to $6,000 is going to need work. Can you do the work yourself? Do you have the extra $1,000 to $15,000 to get it in running order?
A trailer will cost less to get in running order (no engine), but you'll be putting that additional cost into buying a truck.
Do both you and your fiance have jobs? If so, how do you intend to get to those jobs? With a motorhome, you will have to move your house every day to get to work unless you have other transportation.
The expense of gas for the motorhome or truck will be more than your current expenses. The motorhome will get you no more than about 10mpg. The truck towing the trailer probably won't be much better.
Do you have enough funds to add solar, a generator (with additional fuel), and/or electric bills to keep the RV cool in summer and warm in winter? RVs are not insulated like houses and apartments.
Do you have enough funds to pay for the propane use? You're either going to pay for propane or electricity to run your fridge, stove/oven and water heater.
Yes, people do it all the time. However, unless they have a lot of savings built up behind them, they are living paycheck to paycheck without ever getting ahead. They may have family to fall back on if something goes wrong and they need a place to stay - if your trailer needs professional work done, you lose your "house" for the duration; if your motorhome needs professional work done, you lose your "house" and your vehicle for the duration. If you don't have a support system (monetary or otherwise), you may find yourself stranded on the side of the street somewhere in a broken down RV.
Do you have plans for the future? What happens if you or your fiance gets sick? What about kids? An RV Park that you might see as doable now may likely be completely unacceptable with a kid in tow. Again, the folks who make this work have put a lot of work into building a support system in case of failure; those who don't are living on the streets not much better than homeless.
