This is a 2 part answer to your 2 part question
1. I wouldn't use paint at all inside the enclosure, latex paint offgasses really bad (ie. toxic fumes) and I believe it could offgass for months possibly a year in an enclosed space. Think of how long it takes for the smell in a new house to go away, and a house has a lot more air flow/ventilation than an enclosure does. Most people use latex paint in their homes, while living there you may not notice it because you'd get accustomed to it (the smell), but as a guest who's not there on a regular basis you can sometimes notice it for a long time.
2. As far as varathane goes, if it's a melamine cage, don't bother, if it's a pine,oak,spruce or whatever it's ok to varathane but i'd let it air out for a long time, maybe a month or 2. I may be wrong in answering part 2 of this question because i really don't know 100% for sure but i'm quite certain on the first part of the question.
Hope i've helped a bit..
Can anyone else substantiate this?