I have really, really sensitive skin. I use Dove sensitive skin beauty bars and have for years and years. I used them on my face and body with no problems. In the last year I've found that my face has become more sensitive (which I never thought possible) and even the Dove was very drying. I switched to a Eucerin hydrating face cleanser and it's very gentle. I found it at Christmas Tree Shops, but I know Rite Aid and other drugstores carry it. If you sign up on the Eucerin webpage they'll send you coupons, and Rite Aid often has their items on sale. I use Purpose moisturizer with SPF 15. Again, it's very gentle. I tried several moisturizers and many of them made my face "burn" or break out from the sunscreen in them. (and my derm. insists I wear a moisturizer with sunscreen because I'm so pale!) It's about $9 a bottle at
Walmart but I get about 6 months out of a bottle. (then I turn the bottle upside down and squeak another month out of it...the darn pump doesn't get the last bit out!) I had sticker shock at first (as a kid I used the generic oil of olay at Walmart for $3 a bottle), but I figure I'm worth $18 a year for healthy skin.
If your skin is normal, I suggest trying a Dove beauty bar as a cleanser. They're very inexpensive and the sensitive skin one is very gentle. I just have freaky skin.
If you're concerned about a moisturizer/cleanser affecting your face (lucky you with normal skin!!)

you can buy it at Rite Aid the first time you try it. If it gives you a rash or you just don't like it, you can return it there. Whenever I try something new I get it at Rite Aid. I've had to return products before that irritated my skin, and their return policy for cosmetics is good. Once I know it won't bother me, then I get the product where ever I can find it cheapest. It's worth the extra money for that first purchase knowing I won't be stuck with a product I can't use.