first off you dont want solid rubber 700c tires. they are incredibly unlikely to mount and stay put, and they will shake and vibrate you and your bike to death.

the alternative in the modern cycling world is a set of tires with 5mm or so of built in flat protection system. check out some of the schwalbe tires or seca-r. be sure to run the tires with 120psi or whatever the max psi is. the high pressure and flat protection strip will keep out most of the glass and such you might run over.

also be sure your rims or tires have no burs or damaged edges and that you are installing the tube correctly. and carry a co2 cartridge and valve with sealant included in the cart for the quickest get up and go tire inflation and fix in one shot.

if for some reason you have to ride over lots of glass, gravel, thorns and nails, try some bigger tires with some thick tread on them.