In reply to olddirtydoggy:
Salomon do some really good hiking shoes but it seems like all the non-waterproof options on their website are low shoes and all the hi-tops have some kind of waterproofing.
I'd agree with others in that if your primary reason for getting hi-tops is to keep stones out, then a light pair of gaiters and a low-cut shoe would be better. Certainly a lot less sweaty.
I had this setup for hiking the Appalachian Trail and it worked really well. Was pretty economical and very functional. If shoes got wet, they dried very quickly. Goretex would have been a total trench-foot nightmare.
I used Dirty Girl Gaiters but there are now many brands mimiking these, and any sort of lightweight spandex running gaiter will do. Mine just had some stick-on velcro patch for the back and a single lace-hook for the front. Put on like a sock, prior to the shoe. The velcro quickly came off but the elasticity of the gaiter kept it exactly where it needed to be on the shoe. Kept all manner of stone and sand/dust out.
Shoe was the Eskape Aero and although not available any more, it looked very similar to a lot of their current offerings.
I think at the time I paid less than £50 for the shoes and about £20 for the gaiters. Bet that's gone up a bit! I got over 2000 miles out of 2 pairs of the shoes and a single pair of the gaiters.