56-58cm top tube (centre to centre), depending on whether your arms are proportional or a bit on the lanky side.
You could probably pick up a semi-decent old steel machine for that much.
You'll get better quality bits that'll last longer - you might have to make a few minor concessions, like downtube shifters instead.
Bit of a longshot, but someone over at fixed.org.au might have something taking up space in the shed. Worth a try.