No, you can't apply for PR Card before landing. What you can do is update your Canadian based address - if you know it in advance - using ECAS before you land. And once at the border, the officer will ask you what your Canadian address will be and you'll further confirm with them.
If you don't know your Canadian address before-hand and during landing, then you have up to 180 days I think it is to update your address in ECAS online for PR Card purposes. Then they will mail the PR Card to that address after normal processing time.
Re: original post, your first and most important obligation is to go to a Service Canada location immediately upon landing and get your Social Insurance Number. SIN SIN SIN! That is step #1 after landing. You aren't able to utilize your Canadian residency until you get your SIN and its a good idea to memorize it and make it your own. The SIN is your key to any employment activity, banking, social services, and it is important for basic things like credit applications even if you're at a store and just want to purchase goods on credit.
*Everything else* comes after that, you already have a good idea based on the list I read. Go to the provincial services offices and get either an ID Card or Driver License if you already qualify, and get your health card. Sometimes you can do this at the same agency, but here in Manitoba I had to go to two offices for health and then driver license and/or provincial ID.
Once you get these basic items, you can then use your COPR and SIN and Provincial ID/driver license to start your life and create a bank account, phone service, etc. Banking, utilities, etc. come last. You need your SIN, provincial health and ID first. And for those that have a 3 month wait, go to the health office and request information anyway. They can at least show you what to do, and maybe assist in getting private coverage if needed.
