Yup, pretty much this. This is one of the big reasons I'm asking for recommendations, to get a list of actual names to try at the range. I appreciate the suggestions so far!
To anyone trying to bring gun control into this, please don't. Many countries allow firearm renting/purchase for sport and that's pretty much all I'll be saying on the subject,
as it is not relevant at all. I've long been a fan of archery and that hobby has simply grown to include more weapons.
There are too many replies to respond to everyone individually, but to answer a few questions I've gotten:
I kind of find rifles intimidating and am not sure I want to own one, so I'm probably looking for a handgun. Although, I think the gun I had the most fun with at the range was some kind of a bolt-action rifle. I liked needing to place a single accurate shot and it felt..."fluid" needing to load another bullet into the chamber with the bolt. I'm really, really not familiar with firearms so I have no idea who manufactured or know else or anything about it really. Sorry, I never thought I'd even be here asking for this kind of advice.
Regarding training and safety, I took multiple classes at the range.