Hard Cases are junk. The casing peals away after only limited miles.
The best tire for you is the Schwalbe Marathon Supreme, lightweight, but with unsurpassed puncture resistance. The thinest Supreme, however, is 35 mm (actually 37-622). If you want a thinner tire then I would suggest a Marathon Plus, heavier, but cheaper. The same level of puncture resistance.
http://schwalbetires.com/node