Let me save you.
The bike looks to be in good condition. It will be steel, which is a lot heavier, and subject to rust. Cheaper bikes are still made from steel, although in the +350$ range they will most likely be aluminum, and above +600$ will go into the carbon fiber fork/seat posts, then above +800$ will go into full carbon fiber.
You shouldn't have any problems with the shifting - these older bikes use 'friction shifting', as opposed to indexed shifting (i.e the ones with the 'click'). You find the gears 'manually' with friction shifting.
I can see right now that the handlebars are at the wrong angle, the stem is quite long (but has to be a decent length to give room for the shifters), and that the brake levers are a little low for my taste - but these are extremely easy fixes.
I think it's quite odd that they didn't include a size. You definitely need to find out the frame size before making any decisions. There are various sources online to find your correct height - but if you pretend to be interested most bikes shops will do a 'rough' fitting to see which size frame you should be sitting on. Professional fittings are ~200$. Correct riding height will have your knee bending at a 20-30 degree angle, you should have a slight bend in your arms with your hands on the hoods as well. It gets a little bit more in depth than that on pro fittings, but I won't go into that.
Also, keep in mind that these are probably 27" wheels and 1" tires. Nowadays all road wheels are 700c and the most popular road tire is probably around 23C - a quite bit skinnier than the 27x1's. The brakes on these older bikes don't stop as well either - in the rain you'll be wanting to jump off - something I experienced on my old 77' fuji I restored last year (even with new pads).
Anyways. As a lasting impression - remember that there is a difference between being 'vintage' and being 'old'. I think you could get a much nicer, newer bike - that would climb hills easier, and get you going faster for a little more. Go ride a few bikes at a shop, and then decide if you want to go the old route.
Just make sure the bike FITS!