I rode a fair bit as a child. Stopped in college (didn't even take my bike with me), briefly dallied with it in my mid 20s for two years, dropped it again, and then picked it up much more seriously, and probably for good, in my 30s.
I'm not sure where you live (urban, suburan, small town, rural). But if you have access to any kind of non-downtown city streets, it's great for getting reacquainted with your bike in a low traffic, low stress environment. I would have never re-started my biking if my only option was a high-speed road - I would have been too nervous. As you become more confident dealing with traffic, you'll start to learn how to ride with traffic, doing stuff like making eye contact, communicating, and taking the lane.
For your current bike, if the tires don't stay inflated, just get new tubes. They're cheap, usually about $5-10 per tube. You'll need a pair of tire levers to change tires, but those are cheap, too, and worth the investment. Youtube is filled with videos on how to maintain your bike - it's a really underrated resource. Like others said, check your gears & brakes. All are adjustable. Again, a bike book or some youtube videos will get you to where you need to go.
Also, don't get discouraged by your bike. It's probably not sized correctly, and probably ill suited for serious climbs. Definitely consider a new (or better yet, a new used) bike before going back to driving. There's plenty of used bikes to be had on Craigslist, EBay, or even in some bike shops. If you're not doing serious riding, forget a road bike. Get a decent hybrid with no suspension - that crap will just suck away energy going up hills. But the flat handlebars, good gearing, and upright posture is a good way to get back into cycling. They're also more versatile in case you want to start hauling a trailer for groceries. My new hybrid cost me $360 for years ago, but being more Mustachian today I'd probably see what $200 gets me in the used market.