Installing a gray tank isn't a big deal if you're opening up the belly pan for other work and are ready to redo a bunch of plumbing, but it isn't necessary for camping. You can get an external gray tank referred to as a "Blue Boy" that will let you collect gray water in that at a campsite, then dump that water at the dump station before you leave. They typically have rollers and a handle that you can hook over the hitch ball and tow to the dump station with your tow vehicle if it's farther than you want to walk dragging 25 gallons of bathwater.
A few parks prohibit the use of blueboys, but those are usually the snobby ones that also prohibit RVs over 10 years old without special dispensation from management. I avoid those anyway, and I have a (tiny) gray tank.
When you're ready to look at a trailer in person, take a copy of the used trailer inspection checklist.
It's a great resource, it'll remind you of things to check and may be useful to read in detail before you call and ask questions about used trailers as well. You might also consider looking for a volunteer inspector when you get really serious about one, there's a search function for inspectors on the Portal page about halfway down the rightmost column.