Game stores usually have adventurers league, or organized play events. These are usually more constrained, story wise, and focus more on combat. D&D itself tends to fall into combat heavy games as a byproduct of it's ruleset but it doesn't have to be.
D&D is the most famous example of the hobby, but without branding you can call it pen and paper roleplaying, through which there are actually many games to explore.
Back to D&D, as it is a good entry point to the hobby, the current edition is 5th edition, or 5e. To get started, I would acquire and read through the 5e Player's Handbook. You'll also want a D20 dice set, with at least one die with each number of the following sides... 4, 6, 8, 10, 12, 20. You'll want to learn to identify them at a glance as well. People who cannot figure out what dice to roll when someone asks them to roll 2d6 are something of a running joke. It's kind of expected your first couple times, but it eventually becomes expected for you to know your dice. Having your own pencils is also a plus.
For characters, in some instances you will need make your own. In others, the person running the game will have premade characters that you pick from. The best way to know is to ask the person or people running.
If you see something at your local game store, go ahead and ask if you can watch for a bit because you are interested in getting into it. Most people are happy to let you do so.
You can also try listening to podcasts of people playing. Critical Role is a popular one right now. Though I will say that those are much more organized and professionally done than the average game I've been to.
