If it's vinyl, any good vinyl cleaner/conditioner will work well on it. Look where pocketbooks or other small (not swimming pool liner size) vinyl items are sold. Even the larger stores like Sears, Penny's, etc., may carry some product they recommend. (The conditioner part is what will keep it from drying out - a cleaner without a conditioner will cause it to crack eventually. But it's always going to feel a bit slippery unless it's pebble-grained, in which case even if you rub oil on it, it won't feel greasy. Smooth vinyl just has that "there's something slippery on it" feel to it. Especially when it's new, since some of the elasticizers are still coming out of the material, keeping it wet and oily even if you use an oil-removing cleaner on it. You clean it off and more comes out. It can take 6 months to a year for fresh vinyl to stop "sweating".)