No agency would object to your traveling with a partner. If you want more space, like a two bedroom, there is usually a payroll deduction on the order of a few hundred dollars a month.
Benefits are not as good as staff. Period. Some agencies will have a 401 plan, but very few have good health insurance. Consider COBRAing your current insurance. You might also consider per diem with your current hospital and come back and do a few days between assignments to keep your insurance up.
If you Google Highway Hypodermics and the top ten agencies, you will come up with a list of agencies. I don't usually post this, but since the major criterion of this list is benefits, it will be a good place to find your best fit. Agencies that have a lot of benefits tend to be the large agencies. One thing you need to learn about travel is that hospital pay an all inclusive bill rate. This means if you want benefits, it comes out of your pay, i.e., lower hourly rate. You are paid out of a fixed pot of money and have to choose what your priorities are.
You have exactly the right reasons to go traveling! It should be more about the experience and lifestyle than the pay. If the pay and/or benefits turn out well, that a plus.