I've gotten back into running, and I'm experiencing some "runner's knee". I bought the patella straps, but I feel a complete sleeve would be more beneficial.

The funny thing is after wearing the full knee sleeves that I use for deadlifts, after doing a heavy deadlift workout the knee pain went away completely.

I want something that will hold tight around the knee and not slide down. I have also scaled back on the distance (went from not running anything over 1/4 mile to a 9 mile run in 10 days..at 36 was too soon).

Thoughts:
https://www.amazon.com/Venom-Knee-Sleeve-Compression-Brace/dp/B01N9HPFEV/ref=sr_1_6?rps=1&ie=UTF8&qid=1546349708&sr=8-6&keywords=knee%2Bsleeve&refinements=p_85%3A2470955011&th=1

I would concentrate on building back into running in a manner that doesn't cause pain rather than trying to mitigate the pain with a brace. It seems like you know what caused your problem, so work on that thing. I'm sure the brace will help now, but nobody wants to run long term big miles with a brace on.

I use a Mueller knee strap. However, the biggest reason that I feel that my runners knee went away was being better about how quickly I increase mileage. I also felt that shortening my stride helped some too.

I agree with the post above.

It's your knee right now but could easily be your shins or something else next if you aren't smart about your training.

Anecdotal here, but I found that mild lifting and squats improved my knee health when I got back into running. When I did run with some knee pain, I used a simple neoprene sleeve and found that the added warmth and compression helped keep things in check. I haven't run with a sleeve in a long time, but I keep one in my running bag just in case.

I'm the same way. Again after heavy squats this morning, my knees feels great. I've reduced to just 5 mile runs for now and will add 1-2 miles increments when the knee pain subsides.