Nowhere close to "knowing it all"
But thanks anyway ! ;-)
There are no single "best routes" as such, but given you limited time at Lake Tahoe I would take US 50 through the Eldorado National forest and stop at the Gold rush town of "Hangtown", now known as Placerville. I have not been there but it looks pretty cool !
From Tahoe you can head across to 395 South to Mono lake and into Yosemite on Tioga pass but as has been mentioned many times, you have a lot of ground to cover and to detour to Bodie and /or Mammoth will add a lot of time to your day and take it from Yosemite. The Tioga pass has many stops along the way and is a slow going mountain road. Perhaps you should just wait and see how things unfold along the way instead of deciding on each detail.
On the junction of 395 and Tioga there is a gas station where it is a good idea to top up your tank before heading into Yosemite. If you drive to the top of the hill alongside the gas station you can get some nice views looking down on Mono lake from the car park. If you are getting hungry at this stage there is a diner inside the gas station called "Woah Nellies Deli" that serve up good food !
I have probably said it before, but go up to Glacier point in Yosemite, the views are "jaw dropping" wonderful. I would take the 41 through Oakhurst to Fesno, but if you are hoping to drive from Yosemite to Fresno, fly from Fresno to Page and visit Antelope canyon and the Wave you will need to take Superman with you ! [Lol ] Up to that point your trip is fine, but you are going to have to decide whether to go to Page and Antelope canyon or Phoenix for the Grand canyon but doing both options in 2 day's while flying from Fresno and picking up and dropping off rental car's are out of the question.
You will have a great trip if you don't overdo things and will have a great excuse to re-visit at another time. I am afraid I am nowhere near "knowing it all" and that's as much as I can help you with. Somebody may come along with lodging options for Tahoe etc but I would use various sites on the Internet to locate places that appeal to you and your budget.
Have a great trip and please drop by and share your experience with us when you have completed your trip.
More tough choices. [sorry]
In my opinion the first part of your journey looks great up to and including the 1st Oct, then the problem continues I'm sorry to say. I am not sure at what time your flight leaves from Phoenix to home or where you plan on stopping the night of the 2nd, but it is 5 hours plus from Phoenix to Page and another 5 hours plus back, so more like 11 hours driving plus Sedona, Antelope canyon and the Wave and no Grand canyon [?] Not possible I would say.
Solutions ? First of all, if your friends will meet you in Page then to drive from Vegas >Page >Phoenix is the same distance as going to Page and back from Phoenix, so you can save having to fly from Vegas. The Wave is something I would love to do at some time but have not had the time to do so yet. It can only be visited on permits and there are very limited numbers and I doubt you will get one now, unless you turn up early morning and join the "walk in" lottery for a permit. If then you were fortunate enough to win a lottery ticket you have a 3 mile hike in and a 3 mile hike out and a large chunk of a full day gone ! [You can see where this is going ! ]
details here.
To me that leaves 3 options,
1] Drive from Vegas [early start] and meet your friends in Page for an Antelope canyon tour in the afternoon and head towards Phoenix. [Sedona?] A very full day but you could continue beyond Vegas from Death valley[?] on the 1st and start out the morning closer to Page.
2] Drive from Vegas early [over Hoover dam] and meet your friends at the South rim of the Grand canyon and stay near Sedona.
3] Fly to Phoenix from Vegas and travel with your friends to Sedona and Grand canyon.
Purely based on your time restraints I would go for option 2, I know this because I have made similar choices and Antelope canyon and the Wave remain on my "bucket list" but when I do get there I want the time to be relaxed and enjoy these "other worldly" places. Of course that was my choice and it's what you want that is important, or at least from what is possible.
You are getting there so take another look and tie up those loose ends and enjoy !