You'll probably get better advice from the others as to how to address the combination of dry skin and acne. My skin wasn't too dry during the acne years, so I used Accutane. I have no idea whether it's even on the market these days - this was longer ago than I care to remember
But my thinking then was that acne was a more serious problem for me than dry skin...so I fixed that first.
You may well need to try several different moisturizers to find one that does not aggravate your acne. Different products work well for different people. (My spouse's skin is basically similar to mine, but we have to use totally different products.) So don't get frustrated if at first you don't succeed.
As far as tanning goes? Don't. You should definitely be using sunscreen whenever you spend a significant amount of time outdoors. (I use a moisturizer with sunscreen built in.) Yes, it kinda sucks to be permanently fair-skinned. However, the alternatives are far worse: terrible wrinkles by middle age if you are lucky, melanoma if you're unlucky. And in the short term you'll just aggravate your dry skin issues...