I think you should fix the bike up. I've restored several old bikes, including a Schwinn that looks like yours (but not as good) and it should not cost all that much to get it in good riding condition.

You have to repack all the bearings, clean and lube the brakes, install new pads, soak the freewheel in kerosene, let it dry then lube it with motor oil.

I use White-Lightning for the chain, Phil Woods grease for bearings, and silicone spray on everything else.

I would think twice about stripping off the paint though. It looks pretty good to me and "NO OTHER" paint will be as durable as what they did at the factory. If you try to spray it yourself, it will be too soft and scratch and peel too easily. Body shop paint job...maybe, but for my money, I'd just touch up what you have.

Good Riding!