25 days and 5 countries already, you have your schedule full.
Stonehenge is worth visiting but you will need a full day if you want to do it the cheap way.
Same with most of the places on your list. unless they are in the middle of a big city, so do not plan more before you are there.
You can easily add more when there, but if you have so much planned that you can not do all you will not like it at all.
You may even have to drop one of the countries from your list as 5 days per country is not enough if you want to do more than just one city per country.
To get cheap, book ahead, check out hostel booking sites and read the reviews.
Learn to cook before you go, so you can make your own meals from cheap (super)market supplies and enjoy eating. Otherwise cheap will be the local version of fast food, not healthy in the long run.
All places you want to see are to be seen on tours but most or all the time you can take local buses and sometimes trains and get there for much less.
Search for Transport direct for UK train/bus/coach travel and Bahn.de for rail and bus travel in Germany and for train travel in most (or all) of Europe. And seat 61 for information about rail travel and how to make a rail holiday working. Specially good page about rail passes.
That's a lot of travelling in 25 days. Are you sure you are aware of the distances involved?
Get travel guides for backpackers & hostel travelers, read them, and follow the advice. The public library will almost certainly have a number of old travel guides, so remember the prices will be outdated (too low).
Consider joining SERVAS as staying with hosts will save you a lot of money for accommodations in addition to being a good experience. The hosts can also direct you to less expensive restaurants, etc.
http://www.servas.org/
If you stay at hostels then try very hard to make a reservation. At least print the info for the hostels where you want to stay and call before going there to verify if hey have room for you.
Check with your health insurance to find out if it covers you in Europe 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. 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...
Don't let yourself run completely out of money, and remember things ALWAYS cost more than you expect.
European countries have become semi-hostile to "backpackers". The Immigration Officer will evaluate you on arrival and they DO have the authority to have you literally put back on the aircraft if they think you might be "trouble".
Ways to avoid looking like "trouble";
1. Get your hair cut or done. Get a beard trim if male.
2. Dress reasonably well for the flight to Europe. The equivalent of a polo shirt and khaki trousers is fine.
3. Have a reservation at a regular hotel for your first night in the city where you arrive. Something like a Best Western is fine: www.bestwestern.com PRINT the hotel reservation before leaving home and have it in your carry-on. You can stay in hostels or with SERVAS hosts the rest of the time, but have a reservation at a real hotel for the first night.
4. Required is an airline ticket leaving Europe within the 90 day limit. Have a copy of your airline itinerary in your carry-on.
5. If you don't already have a major credit card or Visa/MasterCard debit card then get a pre-paid AMEX, VIsa, or MasterCard debit card that has your name embossed on the card.
For example:
https://www.serve.com/?SOLID=4AMEX&extli...
6. PRINT the travel medical insurance information and have it in your carry-on.
7. Get $300 in 10 & 20 denominations of the currency of the country where you arrive in Europe (it will be British Pounds if you fly first to the UK). Get another $300 in Euros as all the continental countries you plan to visit use the Euro. Keep the rest of your money in your account or on the pre-paid debit card.
There is a small chance the Immigration Officer will question you closely about your visit, even though you are only staying a little longer than the period for a normal vacation of two to three weeks. If that happens, show them your airline itinerary, hotel reservation, hostel plans, SERVAS info, travel medical insurance, cash & cards, and rail pass. Be nice as the officer is doing their job. It should be OK if you follow my advice.
Other hints;
Don't take anything that needs a voltage converter. Most electronic devices accept any voltage and all you need is a plug adapter for wherever you are going. Electrical devices like hair dryers can be purchased after arrival.
Create a Skype account and load the Skype app onto your phone. Have the friends/family you might want to call do the same thing so you can call them Skype account-to-Skype account. You need wifi, but that will save you from paying incredible amounts of money to call home. Wifi is widely available in Europe.
Call your home cellular provider and activate international roaming, even if you expect to mostly use Skype. Using your home cellphone may (or may not) be expensive but having the option can be important.
Scan copies of your passport photo page, other ID (ex. driving license), and the fronts & backs of any credit/debit cards. Send the images to yourself via e-mail and save them in a folder. Same with the travel medical insurance, airline itinerary, and railpass info. That way, you have access to the information via any computer connected to the Internet.
Use an under the clothing security belt for your passport, most of your cash, and most of your credit/debit cards. Only keep in your wallet or purse the cash and ID you need for the day. This is an example, but they are sold in luggage shops:
http://www.travelsmith.com/travelsmith-rfid-blocking-hidden-belt-pouch/792209
Take your home driving license (even if you don't expect to drive) or state ID card as you can probably use it for daily ID.
If you have a student ID - even from the previous semester or school year - then take it. Students get many more discounts in Europe than in North America.
Pack a complete change of clothing, basic toiletries (www.tsa.gov), and a basic first aid kit (Band-Aids, headache tablets, sinus tablets, eye-drops, Pepto-Bismol, and Alka-Seltzer) in your carry on. Checked luggage is rarely delayed, but it does happen and being prepared eliminates a lot of the inconvenience.
Good luck!
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