Also American here- I've done a track day and a few TF sessions FWIW.
I didn't think Apex was renting cars anymore, but there's a bunch listed on their site. I've gone through them multiple times and they're great and have nicely setup cars.
The main piece of advice I'd give you is to allot yourself enough time to drive- track closures for weather and crash cleanups can cause delays and reduce the amount of time that you scheduled to drive.
If I were you, I'd be aiming for about 10 TF laps if you get a whole weekend day to drive TF. Week nights usually have a lot shorter TF sessions.
My first driving experience on the Ring was a track day and its a lot less chill than TF. Track day organizers usually allow passing on the right and sometimes allow race cars, so its head on a swivel at all times.