Just bought a new amp, because I read somewhere that it's what I really need.

It's a brand new Marshall TSL 602. It's a combo amp and it's all valve.

I've never had a valve amp before so I don't know if this is normal, but when I move the amp there's a sound of something moving inside like a metallic springy sound. Is that something valve amps do or is a visit back to the shop in order?
Spring Reverb, perfectly normal.
“Ignorance more frequently begets confidence than does knowledge.”
Charles Darwin
The same thing happened to me when I first moved my Mesa. First I was scared, then I realzied what it was and thought, "Holy shit, this is awesome." Used that sound as an intro for my old band's songs.
Gibson Les Paul Studio
Highway One Telecaster
Dean Evo
Mesa F-50
Laney GH50L
Vox AC30 C2
Ampeg V2
Quote by Arby911
Spring Reverb, perfectly normal.

What Arby said.

Perfectly normal.

I happen have a picture of a reverb tank handy. Those 2 long silver looking things are actually springs that are stretched across the length of the tank and add a bit of 'space' to your sound or 3 dimensional feel for lack of a better term. It is somewhat twangy and has a slight slight delay to it.