Can't see the wood for the trees !
Hi there.
We have all been there when planning your first trip independantly seems a quite a daunting task, but once you start separating all the things to be considered and work on them indivdually, things become much clearer.
Don't let the planning put you off, it's just the start of the adventure, allow it to be fun !! [And we're here to help]
You already have an idea of places you wish to visit, so with those dots on the map you can see how you can best join them together, with other areas of interest to you. As mentioned a loop would work well and the City that offers the best value airfares and car rental combo makes the most sense. So for instance start San Fran, a couple of days along the scenic coastal route to LA and then inland towards the GC and Monument Valley. To get to Vegas you could head into Southern Utah [Zion NP and possibly Bryce Canyon among other options] and from Vegas head across Death Valley and up to the Tioga Pass [CA120] near Mono Lake and cross the Sierras into Yosemite before finishing back in SF.
Once you have your start point, search for car rental deals and work on your itinerary. You don't have to book lodgings in advance, some like myself, who are on a bit of a time crunch like to know where they are staying for the night, where as others like to 'Wing it'. You will always find somewhere to stay, but it could add time finding them in the summer and as mentioned, particularly near 'Hot spots'.
Here are a few of out favourite threads to help you along the way. As your plan comes together keep asking questions and we can help 'fine tune' the smaller detail.