Sorry to arrive to the party late, I've been on Differin on and off for the last decade or so (broken up by periods of alternative treatments and Roaccutane, which didn't stick for me). Firstly, see if you can substitute the gel for the Differin Cream next time you pick up a prescription, or the next time you see your doctor/derm. Its much nicer on the skin than the gel.
Cleanser: I use Neutrogena bar, and my derm recommended that, Cetaphil liquid or bar, or a soap called Sapoderm, which contains triclosan. It seems contrary to typical beauty knowledge to use soap on your face, but they're so similar to other surfactant cleansers that its about the same anyway. Soaps also tend to rinse clean, which is helpful too. If you've since found that soap/foaming cleansers are too rough, consider using oil cleansing or cold cream. Yeah, using oil on acne prone skin seems a little odd, but they are good at preventing irritation, which is your primary goal.
Moisturiser: Neutrogena Oil Free Moisture is my rec, whichever formula takes your fancy. It does what it says on the box without being irritating. The keyword is: Boring. If I need super ultra moisture, a dab of cold cream. I look gross, but it calms irritation and dryness.
Makeup removal: Try a two-phase eye makeup remover all over your face to remove makeup, then cleanse after if you want to. The remover will leave a bit of moisture on your skin, and will remove makeup easily, reducing irritation due to rubbing.
Exfoliation: Differin is very exfoliating anyway. I can't use scrubs at all; face washers/microfibre cloths I've had better luck with but only very gently. Chemical exfoliants are worth a go as well, after your skin has settled, at low concentrations. Its really touch and go though, and I've had a few occasions where I've exfoliated beyond my limit and have had red, hot, irritated and (ironically) eventually flaking skin.
Differin is tough to adapt to, but if you take to it well it can be your best friend. I find it helps my skin heal much faster and with less scarring, and it makes it firm, smooth and glowing. Just try to avoid irritation and you'll be alright.