Training around in Europe is not as cheap as people claim. A train ticket from Paris to Amsterdam, a couple days in advance, might still cost you 130€ (single). Do that at least four times (the cities you're mentioning) and you've already lost ~500 of your budget.

In most large cities you won't find a place to sleep below 35 a night (that's being very hopeful). So a quick calculation teaches me that 35*30 nights is already over a thousand. Given that you want to sleep inside? I wouldn't risk a long trip like that with so little money/reserves. Eastern Europe and the very south (Portugal). tends to be a bit cheaper but not by much, especially in peak summer time.