In northern Europe, the weather will probably not be too good in October. I would try and start in late August. The European summer holidays will be largely over, and the hordes of students will be going home, leaving accommodation more available. There is no need to worry about cycling on roads in most places. There are lots of cyclists about and the motorists are usually used to them. (Yes, there are exceptions, but they are rare). Holland, Belgium and France would be a good place to start to see what it's like. You'll learn quickly.
Have fun.