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I used udaily brand and didn't have any issues. It stuck through sweat and lots of movement. I have sensitive skin, and it didn't give me any sort of irritation. If you are going to use tape, I can definitely suggest this brand. The KT brand would never stick once I started sweating.
I had the issue with my knee caps shift laterally while running. Since I was like 10, I've always had knee pain, and just assumed I would always have to deal with it. The tape did help some, but I started doing PT to strengthen my IT band and inner thigh, and legit in like 2 weeks, I stopped having any knee issues. I'm running 40-50 miles a week with no knee pain, and I haven't worn a brace or taped my knee in months.
Some people have weaker quads, so they do quads and glutes strengtheners to build up the muscles around the knee. This link has a lot of the exercises I did. Just give them a try and see if they help any. They definitely won't hurt.