If you have acne-prone skin that is also dry than finding the right moisturiser can require walking a fine line between dry skin and hydration. You should look for non-oily, non-acnegeneic, non-comedogenic products.
Some products have active components such as benzoyl peroxide or salicylic acid. In our view these are better applied separately as topical products as the concentrations are generally too low to be effective when in a moisturiser.
You don’t need to spend a huge amount to find effective products. We like La Roche Posay Effaclar H.