Grammys11,
First read & research. As 1000peaks has suggested, California Fourteeners is a good place to start. There is also a lot of good information on the Mountian pages and in the trip reports here on Summit Post.
A lot will depend on how you want to go about summiting these peaks. Full packs, stoves, tents, etc. or fast & light with only bivy gear? How many days could you go without a re-supply stop?
Over the past several years, along with various friends, I've attempted all 15 of the California Fourteeners listed by Porcella & Burns. Some on single peak outings and some in groups on multi-day outings.
We did Langley, Whitney, & Muir in a three-day trip, you could add Russell to this loop with too much more effort. I bagged Russell on a different trip along with Carilon.
We did Williamson & Tyndall on a leisurely four-day trip.
We took two days for each of the following: Split, Middle Pal & Sill.
We did Polemonium, North Pal, & Starlight over a six day trip that included two bivies. One in the "U-notch" between Pole & North Pal, one at the top of the Clyde Coulior between North Pal & Starlight.
We day-hiked Thunderbolt, but you could include it a traverse from Sill or Polemonium.
Polemonium, North Pal, Starlight and Thunderbolt are the most technical. The approach for these is easier form the west side, especially in late spring or early summer when ice climbing skills would be needed to ascend the U-notch.