What's the frame size? You can measure from roughly the center of the bottom bracket spindle up to the top of the seat tube, and get a basic size for the bike. This will give the peanut gallery a chance to debate about whether the bike is the right size for you at 5'4", and possibly advise on what you could adjust to make the bike fit you.
I'm not personally a fan of just replacing everything. When I encounter an old bike, I try to re-use as much as possible. Every $10 or $20 helps, and getting the bike in a condition to ride it will help you figure out whether to keep it or not before spending a lot of money.
The innertubes are probably OK. Tires, hard to say. Cables can be refurbished by re-greasing them, unless they're kinked beyond repair. The pedals and stuff like that shouldn't be worn out but might need lubricated.
Upright-ness is an important factor, if you prefer it. Riding your existing bike for a while might help you clarify that preference. You can sometimes get some more handlebar height by adjusting the stem within its limit.
If you get a new bike, keep the old one and use it as a training mule for getting up to speed on maintenance and repair. I believe that there are very few things that improve the cycling experience more than being self sufficient for at least basic maintenance, so you don't have to haul it to the shop every time something goes wrong. Once you've ridden a modern bike for a while, it's fun to hop on a "vintage" model and experience the difference. Some prefer the old.
