Maybe I can print the Tardis? That way I will massive space ;)

So 3D print an extension to your flat to store them in! ;D

I don't have the spaaaaace for all of them

You need to make a set of all of them! :D

Phaser: TOS or TNG?
Ship: Which version of the Enterprise?

I still have paint left from Revell, it's either acrylic or email paint, both should work I think.

I think a phaser and a model ship would be cool. You can paint PLA filament really easily with acrylic paint to add some detail. The acrylic paint pens you can get cheaply on amazon are super useful to add fine details.

On a lighter note, which of the things should I print?

DO IT!!!!!!!