Baby wipes are too wet and too abrasive. (Even tissues, the kind you use to blow your nose, are abrasive.)
Use a microfiber eyeglass cleaning cloth. Use eyeglass cleaning solution - spray one corner of the cloth one spray, then use that to wipe off the fingerprints and smudges. Use the dry part of the cloth to dry the screen. (The whole setup shouldn't cost $5 at any optometrist or Walmart's eye center.)