First of all, congrats there and welcome to your new home.
Some things you should do now are:
You need do apply for a SIN number, or apply for a new one if you used to have one as a student/temporary worker. You can go to a Service Canada and do it the same day, it is fast but depends on how many people are there that day, or you can apply by using a form and send it.
Create a new CRA account with your new SIN number, they will eventually link your new account to the information of your old one.
You need to create a new Service Canada account too, remember to save as much information as possible from your old Service Canada account, as the new one will have very little stuff from the old one (kinda like a new person), they are both linked but you just can't see it. I had to call service canada and they had to send me by snail mail some information that I needed from my old one.
You provably need a new health card from your current province(depends on the province). If you are in Quebec you can follow this:
You also need to schedule a call with RAMQ in order to renew your RAMQ card, as you are a PR now. Strangely, they will only renew it for 1 year, instead of 3 years. Kinda like they are considering that you "just" arrive in Canada, even if you previously had a work permit or whatever here. After 1 year, you can renew it normally, for 3-5 years each.
Depending if you live in Quebec(if not disregard this part) you also need to:
In the case of Revenu Quebec. you should call them and just tell them your new SIN by phone, then after a week or so you can create your new account (this wait time applies to CRA too). This is because CRA and Service Canada exchange information once a week, it is at that point that they verify your new SIN, you may encounter error 210 during the creation of your new accounts, this is because not enough time has passed yet).
Also remember to print, sign and save your Ecopr, it has some numbers that your Pr card has not, and some agencies from the government can ask you for it.
Finally tell your bank you have a new SIN and PR status, as you can access other stuff from them and it is useful for tax declaration later on.
That is all, good luck to you and have fun celebrating.