I sanded and did polyurethane them in the 70's.
What is the best sander for the job? What is the best way to paint and what is the best paint for the job? The cabinets are old but very well made. They were custom built in the 50's. I believe the doors are cypress, and the shelves are 3/4" solid pine.

We want to paint it all.

Thanks in advance

How is your old poly surface holding up? If there are no chips or peels you can scuff the surface with a palm sander or oscilating snader. Just scuff so the new paint will bite. A short nap roller may produce fair results, I spray with a Wagner Paint Crew sprayer.

The polyurethane is perfect. I will spray the doors but what is the best way to paint the frame, I do not want to spray in the house.
Should I prime and what is the best paint in your opinion?

If your poly is in great shape priminig is not so important but not a bad idea. I use Zinnser Bulleye 1-2-3 water based for most priming jobs. You want a scubable surface so go with gloss or semi-gloss, water based latex enamel is fine. Oil based paints are good but not needed for this job.