If you want it to be cheap then I'd find an old second hand mountain bike with horizontal dropouts and convert it, would be very cheap if it had a screw on freewheel rear hub cos you could just redish and screw on a fixed cog. Other option would be to get something with enough meat around the dropout to file a bit of horizontal action and tension the chain. Personally I wouldn't go for a road frame because your choice of tyres will limit how much bumpy stuff you can ride and your much less likely to be able to fit V brakes, which I would also recommend.
If you want it to be cheap then I'd find an old second hand mountain bike with horizontal dropouts and convert it, would be very cheap if it had a screw on freewheel rear hub cos you could just redish and screw on a fixed cog. Other option would be to get something with enough meat around the dropout to file a bit of horizontal action and tension the chain. Personally I wouldn't go for a road frame because your choice of tyres will limit how much bumpy stuff you can ride and your much less likely to be able to fit V brakes, which I would also recommend.