My first offroad SS was in 2007, so it was a 29er with disc brakes, just like the rest I've owned. Not sure if you have a preference as to wheel size and brake type. Cheapest frames would probably be a 26er with rim brakes, which is before my time. But Surly has offered the 1x1 for awhile, is fairly indestructible, so might be one to look for. Here's an example:
Great big Singlespeed thread! - Page 63 | Retrobike
And there's 60+ pages more of ideas.