High budget funding, but you don't know how to setup a company? You go to a company formation agent and buy one and rename it. 200 quid.
"They will be needed to sign an NDA but is there any other neccesary paperwork we should look at."
Um. Yeah. You're going to need an employment contract. And some HR policies. And you'll be wanting to get an employment lawyer to look at all this.
" I have consulted with some lawyers but most are not familiar with the technicalities of making game oriented companies along with game copyright and trademarks."
That's because you're thinking they're something special, but they're not. Just go find a proper business lawyer. Not a high street solicitor, an actual firm with a business group.
Are you really sure you're the right person to be handling this sort of thing? This is the noddy end of running a business and you're already resorting to asking internet forums. What's going to happen when you have to fire some of the staff and do it legally? Or work out what the implications are of ditching a publishing contract? Or the really complicated decisions like at what point in a dev cycle to start working on a second product...