You can definitely get the vaccinations earlier! You only need them when you apply for AOS once you're married. If it's cheaper to get it done in your home country, I definitely recommend it.
The ones you need are MMR (measles, mumps, rubella), TD (tetanus and diptheria) and varicella (chicken pox). If you have immunity to those already, you need to show proof that you've had the booster shots recently or you've taken a titres (blood) test showing that you're already immune to it.
I know personally I got the MMR and TD done at the doctor's, and obtained a sheet showing the results of my blood test for immunity to chicken pox.
Hope that helps you out!