The investment you're making is in your mental and physical health, so yes, upgrading your bike is totally worth it. As for the chain; if it's rusty, you can get a new one for not too much moola. You can also get a chain checker for a few dollars that'll help you keep track of the wear. These old mountain bikes are extremely versatile, so whatever you want to do with it, it'll do it well; except for road racing.
As for upgrading, you can upgrade parts as they wear out; you'll get plenty of use from them, and it'll spread the cost out over time.
I think we'd all love to see photos of your sturdy steel steed. Enjoy your ride!