How to go about planning and booking a multiple state trip.

I'm in the UK and want to do my dream road trip around the US. I've only ever booked stuff through the usual websites etc. How would I go about planning the logistics of doing this. and would want to be doing this solo atm.

if it helps the rough plan is;

• enter through NYC
• Yellowstone
• Seattle
• PCH (see the main stops (Yosemite, Sequoia, California)
• Houston
• Home

I'm not against driving and or flying where I need to. I just dont know how to actually plan stops, time etc.