I put a NEW headliner in my wagon without experience and it turned out decent. Not flawless, but presentable and it's held up (not sagged) after many years. Keep in mind, a wagon headliner is more difficult than a coupe/sedan headliner, so yours should be even more doable. Having said that, I've seen a lot of poorly installed liners.
I honestly don't know how an existing previously installed (and old, to boot) headliner will hold up. Are there wrinkles or flaws in your existing unit? If so, I would seriously consider getting a new replacement liner, since you're doing all that work anyway.
If you do get a new one, follow the instructions included. Mine was vinyl using the typical bow system of suspension, so I was able to use a hair dryer to heat up the liner as I installed it. Warning - the dryer heat does NOT shrink the material after installation (like a flying model airplane skin), it loosens it just prior to installation, then it shrinks back to normal size as it cools (after installation.)
I'm going to attempt to paint the existing headliner in my Thunderbird in the near future, but I'm going to leave the liner installed, since the rest of the interior is gutted out. I'm going to use SEM flexible "paint" (in a spray can) and I've been told by a reputable local car upholstery guy that it will work...We'll see. Again, it needs to be a vinyl liner for the SEM product to work. Might not work on cloth, mohair, etc.
If it's possible to pull out the seats AND the chrome interior trim adjacent to the headliner, you might try painting the headliner while it's installed, covering and protecting the rest of the interior and windows as best you can.