Get one that ripens as early as possible.

Decide whether you want astringent or non-astringent.

See if you can find one in the neighborhood that ripens regularly and ask the owner to tell you the variety (probably won't know).

If what you do get doesn't ripen reliably, graft the neighborhood variety to your tree or find somebody who can do it for you.

Ditto all of that. Look at Raintree's website. In their catalog they say that only Saijo (astringent) ripens reliably for them at their location. Izu is listed as very early and is non-astringent. Both are small trees.

They also note that Coffee Cake (pollination variant non-astringent) ripens in climates with cool summers that won't ripen others (more vague....) and Saijo will pollinate it. So you may have some choices, but if it were me, I'd do the homework first as murky suggests above and see if anyone near you has had any luck. Then I'd try Saijo anyway :-)

I do not Believe Saijo has any Male flowers and would not pollinate other Kaki, but unless you are trying a P.V. type you would not really need a pollinator, as most commerially available Kaki do not need pollination to set fruit. Not sure if my Sajio is overly vigorous, but it is one of my larger growing trees. Very Upright. A great choice though however.

I've heard that a persimmon tree isn't too much work, but for what it's worth I got this piece of information from someone in Southern California. Thanks for the tips!

They are certainly care free here. No real pest or desease. I only prune them a little to control size and water when it is really dry.
Most enjoyable. Spring/summer/fall/winter - always look good.
Olga

That's great, yes I've heard pests are not interested in them at all. Thanks!