Those are all good approaches. You can build a good bike for loose change if you are handy with the spanners, I got a couple of very cheap BSOs (bike shaped objects) from FreeCycle, mine for nowt. I made 1 working bike that a friend is riding about when he feels the need (not often, I suspect he gets on it about once a year while his daughter cycles to the campsite shop).
I built a MTB SS for myself for £50 and what I had in the shed, it's great but not everyone has a Pace Mag fork, Hope wheels and hydraulic discs in the shed.
You can do the same or spend a few quid getting better parts in your local areabearing in mind a complete bike may be cheaper than its parts. Alternatively,
Decathlon have a fully built SS bike for (wait for it) £70. Now I know it won't be anything special but it would be fun to boot around town without worrying too much about where you park it.