Are there any community bike workshops or proper old school bike shops near you? These would be the best places to look for a bike to suit you, obviously I don't know what bikes cost there or your budget. They would have loads of boxes of old parts and should be willing to change parts around to suit your riding.
An old, scruffy bike with good components is a much better machine than a newer supermarket special. One of my bikes has it's original equipment from 1988 and still works perfectly, although well maintained, and still functions better than the cheap crap on modern low-end bikes. So you really want low ratio gears for the up and powerful brakes for the coming down, the best option is to go for a test ride. I can't really go through all the different equipment options as there are too many and they change/upgrade so often and it would probably sound like a foreign language to you?
If you are going on picking the bike yourself at the thrift store. Pick the bike up, heavy bikes require more effort to pedal and are a sign of lower build quality. Take it for a test ride, if parts don't work well and you think it can be fixed up then use it to haggle, obviously you need to find someone to do the fixing but a few minutes adjusting gear shifting and brakes goes a long way. If it feels and sounds, squeaks and groans, like a right old clunker then there is little promise in it. A reasonable quality bike should still ride okay even if not perfect. If the saddle is the wrong height (^Details in post on previous page^) make sure it is height adjustable before you buy. The seatpost can seize solid inside the frame if it has not been moved for a long time.
There are two pedaling styles "mashers" and "spinners". Mashing is more common and puts a lot of effort into every pedal stroke, usually accompanied with a bobbing head. This is bad as it unbalances the bike and is also bad for your knees. Spinning means riding in a lower gear, a lot of fast, light pedal strokes much more efficient and balanced. Try to ride with your first two fingers on the brake levers all the time you are moving, reduces the reaction time when you need to slow down, and you can drag the brakes before it gets away from you.
Bigger wheels roll better than smaller wheels but we getting into little details here. If it has knobbly mountain bike tyres and you're mostly riding on paved/hard packed tracks and roads then get some smoother tread tyres instead, saves a lot of energy. Low pressure in your tyres again makes it harder to pedal and gets you more punctures. So keep your tyres pumped up and a little oil for your chain. Dry rusty chain = hard work. Too much oil is a dirt magnet which wears the chain, when it gets too filthy, rubber gloves, rag soaked in white spirit or petrol. Rub the worst of the clag off and re-oil. Every few rides, clean the wheel rim where the brake pads touch, dirt here makes your brakes less efficient. If it has disc brakes never touch the disc at all, if the disc needs cleaning use surgical alcohol only.
Did I mention I like bikes.