My advice would be to go with a Fender mexi standard Precision. Your hands sound big enough and the styles of music you're into fit well with the P sound.
I also recommend that you have it set up with medium-low action by a pro and put a set of flats on it (either chromes or labella 760 FL's). You won't have to fight hard to play it with the low action and good setup. Flats sound great and are much easier on the fingers than rounds. This is something you'll appreciate as soon as you become addicted and start practicing a lot.
What kind of amp are you planning on? Want recommendations on that too?
I also recommend that you have it set up with medium-low action by a pro and put a set of flats on it (either chromes or labella 760 FL's). You won't have to fight hard to play it with the low action and good setup. Flats sound great and are much easier on the fingers than rounds. This is something you'll appreciate as soon as you become addicted and start practicing a lot.
What kind of amp are you planning on? Want recommendations on that too?