Willeke:

If you are European you can buy an InterRail pass:
http://www.interrailnet.com/
That will give you your travel, unless you want to use high speed trains (surcharge) and overnight trains (compulsary reservation, and maybe also couchette cost.)
If you are not European you can look into the Eurail passes, but those are more expensive:
http://www.raileurope.com/rail-tickets-passes/eurail-global-pass/discounts-and-pricing.html
Both passes come in different versions for length and coverage.
See all different versions and work out which is best for you, as in how often and how much time per travel you want to be on the train.

Train and hostels are a excellent combination, you will also meet a lot of people that way.
If you want to camp, doing so while traveling by train is rather hard, as most campsites are far from the railway station and you will have to carry much more gear. It is doable, most campers use cars of at least bicycles.

When you use hostels, next to your clothes you need a towel and in some cases a sheet sleeping bag, (but I have seen sheets for rent in nearly all hostels.) A sleeping bag can come in clever, but is not often needed, specially in summer.
If you go camping you will need a sleeping bag, and a mat, a tent, and likely also a stove, pan, plate, knife, fork, spoon and you can add the rest if you do camp.

About your route, from the south of Portugal to Italy is a long way, you can contemplate a flight, if booked early they are not that expensive.
But you can also take a week to travel back though Spain and the south of France.

At this time a travel like that will cost about €75 (£75, $US100) per person per day, allowing you a modest for the odd drink and sightseeing.
High and mighty you stay in hostels and your travel cost already paid for.

If you travel by car you can cover more distance each day, but you will have to add for petrol/gas, as well as highway toll and cross channel ferry.

For hostels and sightseeing information, and a few addresses of campsites, I rather the Lonely Planet series, but in any case you will need a excellent guidebook covering the area you want to travel.

If you want to travel by train, your only real options lay in going to Paris and south from there, in Spain you will have a few options, but do not count on many trains on all lines, often it is only a few per day.
This railway map you can see where rail travel is doable:
http://www.interrailnet.com/interrail_railway_map
And the German railplanner in English is mostly a excellent help on travel information. It just does not give info on travel to Portugal at the moment:
http://www.bahn.de/international/view/en/index.shtml
So here is also one for Portugal: http://www.cp.pt/cp/displayPage.do?vgnextoid=87cbd5abe2a74010VgnVCM1000007b01a8c0RCRD&lang=en