Mike,
To begin with, is there any possibility you could move your trip to May/June or Sept./Oct.? July & August are not the best time for travel in Europe, as it's usually hot and crowded. Also, especially in Italy many of the locals take holidays in August so some tourist facilties will be closed.
It would help to have a bit more detail about your trip. Will you be going for the entire two months? Which cities in each of the countries you listed will you be visiting?
Regarding the flights, there are a few possibilities. Given your location, you'll probably be departing from YVR, so you'll need to consider which airlines operate from there. Using open-jaw flights is definitely the best idea. At that time of the year, all the major airlines will be offering flights to Europe.
For airlines, Air Canada will be adding new flights to Athens and Spain next year, beginning in June. Air Transat began new direct flights from Vancouver to Rome and Barcelona this year, and I'm assuming those will continue. Flight schedules for next year won't be posted for several months.
Given the countries you listed, I'd probably start in Portugal or Spain (whichever has best flight availability. Travel from Portugal to Spain (or vice versa) via rail/Coach and then budget airline to Greece. Travel within Greece via boat/hydrofoil or perhaps air (if you're going to the Islands?). Finally, budget flight to Italy (probably Rome / FCO). One possibility would be to start in Rome and fly home from Milan. I used that method this year and it worked fine (my flight was Air Canada, but codeshare with Lufthansa).
If you decide to travel via budget flights in Europe, you'll need to PACK LIGHT! Within each country, travel by rail (or in some cases Coach) is the best method.
If this is your first trip, I'd recommend reading Europe Through The Back Door as the first step in planning.
Good luck with your planning!