The cheapest way to travel between most of the countries will be coach, specially when there is a sea to cross.
The shorter the travel, the cheaper it will be on average. And even when it is not cheaper it will be easier for planning the travels.
Best take a map and look at the locations of the countries and your choice of cities.
If you can afford it, traveling by train will be more comfortable and often faster and with more choice of times. Like there will be one coach but 4 trains per day.
How every well you plan you will end up with doubling up or by flying, as Ireland, Sweden, Spain and Greece are sticking out from the main area of your selection.
If you want to see something while traveling, plan a week per country.
Take Ireland. You can see Dublin in a day or two, but the best of Ireland is the west coast, it takes a few days to travel there, have a good look around and travel back to a place where you can go to England (possibly via Scotland or Wales.)
If you plan a week on average, you will have time to get a good impression of the countries you visit.
Many people do try to visit as many places as possible, one or two days in a city and on to the next. When you do that you will see the inside of the trains or buses more than what you come to see, and you will remember very little. And all will be blurred, as all memories will melt together.
Have you considered to buy a rail pass, it's a fixed fee and you can travel as much as you want for e.g. a month.
http://www.eurail.com/eurail-passes
The price isn't that hefty if you compare it to other ways of transport. The benefit of it is also that you don't have to book several days in advance. I used it when I travelled all around Europe (a long time ago). The part that I liked best about it was the freedom that it gave. Got tired of a city/country, just get on the train and go to the next destination. You can then book your hostels/hotels the night before you arrive using booking sites. Note that there also are some night trains that you can use when you want to travel longer distances.
All of the countries you plan to visit are expensive to extremely expensive. You also plan to visit 10 countries during one trip, with Greece and Sweden almost as far apart as they can be and still be in western Europe so your transportation costs will be high. The days of "Europe on $20 a Day" are several decades in the past and you need to evaluate where to go after doing more research on costs for things like meals, housing, and transportation. For example, you need to budget $60 per person per day for meals, even if you plan to buy food from grocery stores.
This was advice I provided recently for a Canadian planning a trip to two or three countries:
I suggest flying first to Ireland or the UK, even if you plan to visit France and Italy. Everyone underestimates the effects (usually called "jet lag") of the overnight flight to Europe and you will be able to cope much better on arrival if you are in a place where English is the language (true even if you speak some French & Italian). Really.
Recommended as a first destination is Dublin. It's not as expensive as London and transportation between the airport and the city center is easy. Ireland also uses the Euro, which simplifies things if you next visit France or Italy. There are lots of flights from Dublin to the continent and you can even take a ferry to France.
Dublin is also a great place to visit/tour and you can see the highlights in three days (not counting the day you arrive and the day you leave), which is also about how much time you need to mostly get over the time change.
http://www.dublinsightseeing.ie/
You need a passport if you don't already have one (you probably do).
Canadian citizens don't need a visa to visit any country in western Europe or most countries in eastern Europe, but always verify:
http://www.skyteam.com/en/Airports-Servi...
Get a Visa/MasterCard-logo debit card for your bank account if you don't already have one. If you can, get a credit card even if it is a supplemental card on your parent's account. Notify the card issuers about a week before you depart that you will be traveling in Europe (important).
Get $300 cash in the currency of the country you will first visit. For example, 300 Canadian Dollars is about 200 Euros right now. Your home bank should be able to get the Euros for you, and ask for 10 Euro notes. Keep the rest of your money in your account and use ATMs to get cash as needed. Only use ATMs from a real bank.
Make a reservation at a hotel or hostel for the first few nights, even if you expect to travel around without specific plans afterward. If you travel first to Ireland then make a reservation for at least your first night when you go to the continent. PRINT the reservations and have the copies in your carry-on.
Many cities in Europe host festivals around the year and the hotels & hostels can be completely full. Make reservations when you can, and the farther in advance is both better and will usually result in lower costs..
Dress reasonably nicely for the flight to Europe. The equivalent of a polo short and khaki trousers is fine.
Check with your health insurance to find out if it covers you outside Canada and pays for medical evacuation to home (should that be necessary). If yes then take proof of coverage with you. If no or not sure then get trip medical insurance, which is cheap and sold by airlines & travel agents. Having travel medical insurance is a requirement to enter some countries (ex. Lithuania & Slovakia). Even if it's not, PLEASE do not skimp on this as an otherwise-silly accident could turn into a crisis if you don't have medical insurance. . This is a link from the US government, but the info is good for anyone traveling outside their home country:
http://travel.state.gov/travel/cis_pa_tw...
If the Immigration Officer asks how you will support yourself while visiting, show the cash, your credit/debit card(s), the hotel/hostel reservations, the travel medical insurance info, and your airline itinerary
Realize Immigration Officers view a teenager traveling alone (includes with a friend) completely differently than they would view the same teenager traveling with their family. Don't look like "trouble" to the Immigration Officer as they DO have the authority to deny entry. .
Take your Provincial driving license or ID card. You can use it for daily ID and keep your passport tucked away.
Take your student ID with you. It will still be accepted as valid over the Summer (maybe even the Fall) after you graduate. Students get a lot of discounts in Europe for things like museum entrance fees and public transit, so always ask.
Join SERVAS as it gives you vetted local contacts in many places, even if you don't choose to stay with a host.
www.servas.org
Call customer service for your cellular service and activate international roaming. Being able to use you home cellphone in Europe may or may not be expensive (ask), but having he ability to do so can be important.
Create a Skype account and download the app to your phone. Do the same for the friends/relatives you may want to call from Europe. Calling Skype account to Skype account is free and wifi is everywhere.
All electronics made anytime recently accept any voltage and all you need is a plug adapter. Don't take anything which requires a voltage converter. It's better to buy things like hair dryers and curling irons after arrival than to try to use your electrical appliances from home with a converter.
Scan the photo page of your passport, your Provincial driving license/ID card, and the fronts & backs of any credit/debit cards. Send the images to yourself via e-mail, along with your airline itinerary, hotel reservations, and travel medical insurance. That way you have access to the information via any computer connected to the Internet, which can be important if something is lost or stolen.
Finally, don't try to visit too many places. It is far better to visit a few places and get to know them than to flit from country to country.
I hope you have a good trip!
You won't have time, honestly.
