beezaur

I am the same height as you, just a little lighter, and ride a 58 cm road bike. I wear pants with a 34" inseam. My arms and legs are a little long, but other than that I am pretty much average build.

Bike geometry and fit is a deep topic, but for most purposes it comes down to these:
- You need to be able to raise the seat enough that your legs are almost straight at maximum extension on the pedals.
- The seat should be adjustable horizontally so that you can put your knee over the pedal with the crank horizontal.
- The handlebar should be approximately at or below seat level, and approximately below your nose.
- Your back should be somewhere around 45 degrees from horizontal.

A lot of bikes deviate from that on purpose for specific reasons (triathlon bikes, comfort bikes, etc.), but that is a rough, general purpose, "get you in the ballpark" type setup for general purpose road riding.

A 58 cm road frame allows me to make the proper fit adjustments so that I work my body correctly. This both avoids injury and allows me to put much more power into the bike.

For better fitting either have someone fit you or get a book. Andy Pruit is a respected authority on health aspects of riding, and has written a good book on the subject. I would recommend such a book instead of a fitter. A professional bike fit will do more for your performance, but this is stuff you need to know and understand yourself for your own health.

My gut insinct is to go to a bike shop for a used bike. You can see it for yourself and it will have been checked out mechanically by someone whose body language you can read.

A lot of those really old bikes will have 27" wheels and will have drivetrains that are more or less obsolete. They might have worn out chains, gears (rear cogs), bottom brackets, hubs, who knows what. A bargain bike could easily turn into an expensive repair job.

When I refurbished my 20-year-old road bike I did the work myself and spent ~$250 in parts. But I had the tools and another bike to cannibalize from.