I travel every 1-3 weeks, sometimes more often.
How much does it cost is an impossible question to answer. I've seen monthly budgets of $2,000 and others of $10,000. I budget $50/night solely for campground fees; I have friends who budget $25/night; I have others who stress if they spend more than $250-500/month; and one family who will ONLY stay at Thousand Trails parks and shoots for a monthly budget of $100 or less. Fuel is a whole nother expense- especially if you're towing a camper with a truck (that's now your daily driver and sight-seeing mobile).
The longer you stay at a campground/RV park, the cheaper it is. Boondocking can be less expensive (of course with the initial investment in a "proper" boondocking setup).
What not to do? Expect that you're camping Fulltime. This is now your home and your life.
What else not to do? Ignore weight ratings. Weigh your setup and be aware of what you're carrying. Now being your home, it's going to be carrying a lot more than you did as a weekender.
Be aware that almost any camper you buy is not rated for fulltiming. Little and unexpected things will break- my most used examples are that I've had to replace drawer slide hardware and the bottoms of drawers.
Also, get a fulltimer-specific insurance policy.