Welcome to RTA!
The routes are all quite safe but some are mountainous and not very heavily populated. I'd recommend you get gas if you have less than 1/2 tank and see a gas station. As I remember, cell coverage is pretty good.
UT-12 from Bryce Canyon to Capitol Reef is one of the most scenic drives anywhere.
To get from Capitol Reef to US-163 you will need to take UT-24 to I-70 to US-191, taking you past Arches and Canyonlands, completing the "big 5".
I'd recommend you buy an annual National Parks pass ($80) on the way into Zion. It will more than pay for itself because admission to Zion and Bryce is $35 and Capitol Reef is $20 without a pass. If you visit any other parks this year, more the better. If this trip is more than 3 weeks from now, you can order a pass online at https://store.usgs.gov/2025-annual-pass with a $10 processing fee. If you are military or a veteran, you may qualify for a free pass.