I generally still just use cotton wool or washable wipes (like mini flannels) and water. To take them out and about, I put a couple into a little plastic ziplock bag. (Actually, I reuse rinsed-out breastmilk freezer storage bags for this, they're tough plastic and a handy size, and I hate to throw them away !)
But we do use wipes sometimes - I got some Waitrose plain ones on offer which seem good, at least they don't have any parabens in them.