European tour - advice wanted

From your profile, I presume that you are a South African citizen and need a visa. Schengen and non-Schengen visa are different procedures.

You are supposed to get a Schengen visa from the country which is your main destination, or if there is no clear main destination, from the country which is the first destination of your trip. So you could apply for a visa from your first planned destination in the Schengen zone.
The visa officials will try to admit genuine tourists and refuse illegal immigrants. Part of the criteria is a coherent premise and itinerary of the trip. So if your premise is spend 100 € a day, let's see where you go, that would be quite unusual but not impossible. The rest of your application would have to be very strong, with clear indications that the money is really yours and that you really will leave after the holiday.

Source: stackoverflow.com