I don't think that the wrist or finger models are always as accurate as the upper arm models.
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I have an automatic inflate Omron that I've used for years. They make many different models, and I think Omron is a fairly good make to buy. They are generally rated very highly for accuracy, but I would stick with an upper arm model with an auto-inflate cuff. The left arm is the preferred arm to use according to their instructions.
It is a good idea to take the new machine with you to the doctor's office, and use it there yourself at least five minutes before the doctor takes your reading. Then compare the results to get some idea of the accuracy of your machine.
Try to check your BP at the same time each day, so you can get a good idea of your average reading. Many different factors can produce transient variations in BP, and what you really need to know is your average range of scores at the same time each day.