You should read some reviews as you'll likely have some personal preferences that will heavily influence your choice.
If you really don't care what the case looks like and just want maximum protection then get a bunker type case like a Griffin Survivor or Otterbox Defender. Basically a big, thick rubber wall that will protect your phone against most accidents. Or maybe you want something more elegant, like a Spigen Ultra fit. A lot better looking and much thinner. But also less protection. Or a hundred variations on either theme.
Likewise for screen protectors. The tempered glass ones offer the most protection but are more expensive and thicker than plastic sheet type protectors. Read some reviews or better, take a first hand look at local stores to see what you prefer.