You can literally turn up and try to start your new life! However, I would probably try to find work in advance. There are many international jobs sites, e.g.:
www.eurojobs.com/
https://ec.europa.eu/eures/main.jsp?acro=job&catId=482
There are, of course, loads more.
As you have recognized $5000 (about 2800GBP) isn't a lot of money so you might have difficulty in setting up a life in Northern Europe where the costs are really high. I've been looking at some other places, e.g. Spain (obviously costs are high in the main cities), Hungary (rental costs seems quite low) and Croatia (awesome scenery/beaches).
There may be other factors which affect your decision, e.g. language, desired climate, food preferences, education for kids etc. I guess you will have already thought about these.
There is also some useful info on this site:
http://www.expatinfodesk.com and
http://www.expatica.com.
I'm sure you have thought about a lot of the stuff that I've mentioned above, but I just thought that I'd share some of the things I considered when I was a thinking about moving to another EU country.
If you currently have a job in Canada, you might want to see if there is anyway that you could be transferred to Europe? That would makes things easier.
Good luck with the move!
CC