The cheap tires I use on one of my bikes are Performance Forte Metro K (K for Kevlar belt) 26x1.25"/559-32 tires and they have provided excellent performance and flat protection. Reasonably light, smooth tread, no on-the-road flats since I started used them 2-3 years ago.
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Bacchetta Giro A20, RANS V-Rex, RANS Screamer