Yeah, it makes sense to travel around Europe using train. Definitely must get one of the train pass. You can get them from STA Travel. One suggestion though is to get the ISIC (International Student Identity Card) first, it allows you to purchase the train pass at 10-15% discount and you can use this card to get student rates at places of interest around Europe. You might also wanna get the HI (Hosteling International) card if you intend to stay in hostels.
Do pick up this guide book, Lonely Planet "Europe on a Shoestring". You can either buy them from major bookshops or borrow it from the national library. One of the best guidebooks around, got 80% of my accomodation contacts there.
What I did last year was travel to Rome, Italy via Istanbul on Turkish Airlines (S$1300 with option of 3D/2N transit at Istanbul, which I stopped over at at the end of my trip before returning to Singapore). Bought a East Europe train pass (travel between Austria, Hungary, Slovakia, Czech Republic, Poland) for around S$450. For Italy, bought a 3000km train pass for around S$200, just nice for 5 persons (S$40 each) to travel by train from Rome to Florence to Venice). Always try to get accomodation near the city or places of attraction, that way you don't waste time/money travelling. Don't be penny wise pound foolish, the money you spend on a better location will be worth the time/money spend on travelling)
Here's my iternery (in case you are interested)
Singapore - Istanbul - Rome (19 hours)
Rome (4D/3N, accomodation: S$30/night at some hostel near the Coloseum)
Rome - Florence (morning train: 4 hours)
Florence (3D/2N, very nice motel at S$50/night near train station and Doumo)
Florence - Venice (morning train: 4 hours)
Venice (2D/1N, cheap and nice hostel at S$22/night near train station)
Venice-Salzburg, Austria (overnight train: 8 hours)
Salzburg (where Sound of Music was filmed, lots of lakes and mountains 3D/2N very nice homely motel at S$22/night near the old town and most places of attractions)
Salzburg - Vienna
Vienna (nothing much to see here, 3 star hotel at S$45/night in the inner ring, near city centre)
Vienna - Budapest, Hungary (5 hours train)
Budapest (exotic place, ex-communist country but really safe, 3D/2N 4 star hotel at S$50/night near city centre, things are really getting cheap from here onwards)
Budapest - Bratislava, Slovakia ( 5 hours train)
Bratislava (Slovakia used to part of the Czechoslovakia, nice small city will many innocent looking and very pretty women, 2D/1N motel at S$30/night near train station)
Bratislava - Prague, Czech Republic ( 5 hours train)
Prague (definitely must go place in East Europe, tremendously beautify city, 3D/2N hostel at S$30/night near subway to all major attractions)
Prague - Istanbul, Turkey (3 hours flight)
Istanbul (very exotic, beautiful place, very friendly people, very safe country, and no they don't attack people who wears English soccer jerseys even if you wear them near Galatasaray Stadium 3D/2N 3 star hotel at S$40/night)
Total num of days: 24
Total expenses: $3500-$4000 (with reasonable purchase of souveniers (S$500-800), visitation of all important places of interests (S$300), 1 restaurant meal per 1.5 day in Italy and Austria (S$20), 1 restaurant meal per day in East Europe and turkey (S$10-S$20))
Perhaps if you are interested, I can tell you more at the next upcoming SEED (12th March). You can also call me at 96226876.