Shorts is one of the few areas of sports clothing i feel you need to spend the money on, shirts... not so much,
I personally favour RonHill shorts, both the patriot and Advance cargo race short imo are amazing, the quality of materials and durability are far ahead of your average nike/new balance etc that you can pick up at JJB etc, but at close to £30 they are not cheap either. if you're willing to spend some money on some shorts to last you a long time, i would certainly look into them. both have the zip pocket, but the advance cargo's have gell pouches too,