Welcome Sadie and Tyt, you're getting good advice so far on gearing. I agree that practicing using the various gears allows you to get a feel for them and how they can help you on uphills or downhills. As a tip I used a flat-as-a-pancake rail trail to test them out so I wouldn't be effected by stop signs, street lights, driveways that would cause me to slow down or stop. You need a place where you can cruise without stopping to guage the effects of what each gear does and feels like.

If you bike has different rings in the front and multiple cogs in the rear, start out on the middle of both and then play with the range in back. Once you have a feel for it, move to the other ring in front (provided you have more than one) and then move the back gears around while in that one. Don't mix up the extremes (hardest front and easiest back or vice versa) at the same time because it puts too much strain on your chain. This is not as confusing as it sounds, it just is harder to explain than to do.

As you ride think about what you like about riding and where you like to do it. Paved paths? Gravel trails? City streets? City walkways? Open roads? Dirt roads? Lots of people around? Solitutde? Some people feel safer around others and some people prefer the serenity of being alone. The various bikes offered these days are a sign of the specialization that occurs everywhere in all things and are designed with a particular kind of riding style in mind. Can one bike suit all those needs? That's up to the individual. That's also why hybrids are available that cross over multiple kinds of riding.

Don't jump into significant purchases until you determine what your needs are because your needs and enjoyment may evolve over time. As your prefered style narrows down over time the choice will become evident.

I second Jobob's advice to try to find others with a bit more experience to ride with, you'd be surprised at the good tips and pointers you will pick up. Most people who ride are willing to help out others and are friendly and helpful. You might run into a group that is standoffish but that's life, keep looking till you find helpful people. Of course there's always TE women around to help.

50's is NOT old, said with authority from a mid 50's woman!