Okay, there's an ad in the local paper for a Mountain Bike. I'm 5'7" in the ancient scale. What size wheels and stuff should I be looking for. Any other tips and hints I'd be grateful for.

I'm 5'7' and ride a 18.5" MTB. All MTB that I know of come with 26" tires.
Tire width and tread patterns, that all depends on the type of riding your going to be doing and is easily changed.
The drive train I wouldn't touch anything less than Deore. Mine came with less and lasted less than 500KM.
Forks that again depends what type of riding your doing, your weight and how cush of a ride you want.
Hope this helps abit

please elaborate... does it not have any at the moment?

If you're wondering if it will fit you:
https://www.wrenchscience.com

and check out their "WS Sizing System"
(link on RH side of page)

-one of many similar sizing aides


ditto.

Sorry, the ad just says "adult mountain bike, good condition Aust$100.00 (US$75+-) That means it's kitted out for sex acts on the road or should roughly fit me. At the price it may not be a bad buy unless it's a Kmart job.

You could lalso look at the 29 inch wheel bikes at your hieght. This make slightly better road bikes. But as pointed out above, you can't really change what the bike has.

Go to a bike shop and explain that you are looking for an MTB and what do they have. Get an idea of fit either from the LBS or at least by sitting on a variety of frame sizes. Then find out what their cheapest reputable brand is, and maybe lay-by it. You'd be much better off.

Personally, I wouldn't consider an MTB at that price. Probably old, probably in less than good condition, probably needs mucho work to get back into shape. People who advertise their bikes also have a fairly overinflated sense of their market value.