
The problem with the 3 year thing is that you must first achieve ILR (Indefinite leave to remain) before you can apply for naturalization and:
"Note that a person living in the UK as the husband, wife, civil partner or unmarried/same-sex partner of a British citizen or a settled person who either arrives in the UK or applies for permission to stay in the UK on or after 9 July 2012 must live in the UK for 5 years (and not 2 years) to obtain ILR"
Therefore, you will be better to wait for PR after 5 years, especially if you don't want to become a British citizen.
Wish you all the best
C