If you are going for looks, or an accurate restoration, get a Briggs flatty or a Tecumseh, if you just want a good, fun rider, for the $$$$, I really don't think you can beat the Honda clone, AKA Predator from Harbor Freight for $99.
I have had a lot of Briggs flat-heads, a handful of Tecumsehs, and a bunch of Kohlers, Kawasakis, 3 Briggs Inteks, and a couple of Hondas. So far as ease of use, easy starting, fast warm up, torque and general reliability, the Predators beat out any of the flat-heads, the OHV Kohlers and are level with the Kawasakis and Hondas.
My Predators start first pull every time, they are warm enough to run without any choke instantly, they deliver great power. Pay an extra $20, and you can get the 2 yr instant replacement warranty. Try to get a Briggs, Tec, or Honda with a 2 yr instant replacement warranty for $120.
If you don't want a Clone, and are not really sold on a flat-head, (like you want to buy American), I would recommend the Briggs Intek. I have them on my aerators, which get bounced and worked very hard. My Inteks last much longer than the flatties I used to run, and start way easier.