I am buying my parents 98 Civic from them. 2 more payments and it will be paid off

I've been driving it and had it on my insurance since Sept. 01.
The tag is due on the 30th of May (my father's b-day). We will be getting the title in July once the vehicle is paid off.
We are trying to figure out what will be the best way to go to get this vehicle transferred into my name?
a) They sell the vehicle to me ASAP (before the tag is paid in May)?
b) I pay the tag before the due date, then once the vehicle is paid off they sell it to me?
Wouldn't I have to get new tags with option "b" within 30 days
...or they just keep it in their name and next year just before May sell it to me
If you guys need more details let me know.....
My b-day is on May 21st if it matters.
Thanks!