Of course if you're loaded ($$$$$) you can do pretty much whatever (look at Emirates Airlines, first class!). Otherwise if you are a normal being on a normal budget (or indeed a student on an even smaller budget) you will want to look at alternative ways. Youth hostels are good - but you are sleeping in a dorm with 4,6, 8 other person or whatever.
An option which I have used and like (though you must always have a Plan B) is couchsurfing****. Sometimes you end up staying in what could be a 5 star hotel it is so lovely. Other times you end up sleeping on the floor (not bad in itself) but in thye place which has not been cleaned for a month...or six and you can't wait to get out of there. Experiences.
I also have made use of a site called Housesitting****. Ok: there are many such and it costs around 20$ to 50$ to sign up depending. I did house sitting in Germany and the US. True, for such you need to have either flexible vacation time or pretty much be retired. But the experience is totally great.
As for mode of travel, I like expedia**** where you also find excellent deals for airfares - hotels - cars pretty much all you need, And at times they also have the "offer of the day" where you have excellent rerductions. Bon voyage.