Sounds like you want an Otterbox Defender for 5S. Fits the requirements stated above, and works with the touch sensor.
About Applecare+: You buy it at the time of purchase, or within 30 days (phone must be examined at an Apple Store). You get two $49 repairs should your screen crack, phone breaks from drops, etc. All other faults are covered for two years (ones that are Apple's fault, i.e. jammed lock button, not yours, such as dropping the iPhone into a pool)