I guess it is easier to get the SSN and open a bank account before findind a job, but with a K1 when do I have to stop working?

You will need either an Employment Authorization Document (EAD) or a Green Card to work in the US if you've entered on a K1 visa. The other option is that some land borders off the EAD stamp in your passport, which will allow you to legally work in the US for 90 days.

K-1 is work auth up to 90 days after entry and employers are required for you to show EAD either by a stamp or card issued by USCIS.

Note: K-1 is not a work visa, it is a fiancee visa for entry to the USA and marriage, K-1 is "Work Auth" primarily to be able to get the SSN, some states are strict in their interpretation of a federal law that requires persons applying for a "license" to have SSN, this can cause a problem with marriage license if only one person has SSN and the other (the K-1 holder) does not.

If you come in through JFK and you get a stamp that allows it you can work for 90 days after your arrival. You then have to wait for your work approval. Most companies won't hire you because of the potential break in employment.

Note: The OP is Canadian, US immigrations handles the paperwork at most airports in Canada, so a flight to JFK will tend to be like a domestic one, and most likely wont go through the POE there, so wont see the Immigrations officer at JFK and miss getting that stamp there.

Search a bit, some of the border crossings have been known to issue the stamp.

Maybe a hamburger flipper somewhere would qualify...?