There are stains, and then there are stains. You get what you pay for with paint and stain. I would only consider an oil based stain and I would only look at the big name companies. I've had good results with Cabot's, but since Lowes quit carrying them, I pretty much just go with Sherwin Williams now. I'm not familiar with any stain that stops bug damage, but then it's never been on my list of things to look into. What kind of damage and bugs are you talking about? Termites will just go around it or under it until they find what they want.
Are you using real wood for the trim? I prefer Hardie, especially if you are going to paint it. If you are going with real wood, be sure to use a top quality primer. There is no such thing as primer being part of the paint. That is just a sales gimmick that means the paint covers better then their lower priced paints. For raw wood, you have to prime. My favorite primer is the Zinsser brand. The 123 is great for most everything. Sherwin Williams also has a very nice primer designed just for raw wood that is very good. I rarely use Kelly Moore, but find it to be pretty good too.
Avoid all the other brands sold at the box stores.
Eddie