As a former private investigator having delt with many people in similar situations. I would recommend not wasting your time.
The root of the problem is that there is no trust. If you pull off the surveillance, either way you lose. Either it confirms she is cheating, or you will continue to be suspect. If she finds out you are doing it, you lose.
The lack of trust, for whatever reason you have it, is enough to suggest this is probably a relationship that is best let go. Without trust you will never be happy. And NOT catching her will not ease your suffering. I dont think this woman is the one for you. If she was, there would be NO suspicion at all.
Good luck with whatever you decide, but you are approaching a cliff that you cant keep from falling off of, no matter what you find.