I agree. Send them an introductory letter immediately that outlines who you are and how to reach you. I would also introduce myself to them in person with a thoughtful little gift. It doesn't have to be significant. Just something small to start to build the rapport.
In terms of raising the rents, I would notify them as soon as possible. Just make sure you follow the rules for the state. If a tenant has lived somewhere over 3 years, you must give them 90 days notice. If it's 1-2 years, 60 days. Less than a year 30 days notice. That goes for all aspects: raising the rent, renewing the lease, etc. Additionally each town has enacted slightly different laws. Depending upon where your rental is located, there may be a rent increase cap. So make sure you are very clear on what the laws are before you take any steps. This is crucial because if you do raise the rent, but didn't follow local regulations, your tenants can challenge it in court. NYS courts tend to err on the side of tenants so make sure you are following the law explicitly and stay on top of the new regulations because they are continuously changing.
Good luck! You got this!