best way to travel

I´m helping two friends that have never been to Europe and I have a couple of questions on how they should travel. They have a low budget!

Which is the best way to travel from madrid to rome?

Which is the best way to travel from Rome to Amsterdam?

I´m also looking for hostels in Rome and Madrid for them both in the city center... any recommendation?

THANK YOUUUUUUUUUUUUUUUUU

Ive been researching travel in Europe lately. I am opting for train travel for most of it, probably going to buy a Eurail multi country pass which includes alot of travel such as boats as well as trains.

You can usually get pretty cheap flights about everywhere nowadays though! If you shop about you can get bargains...