VGK can pick up to 7 goalies. Would you go with that max amount and look to trade 3 or 4 to whoever makes the best offer of draft picks or prospects.

I'd take around 6.
1. Fleury
2. Mrazek
3. Pickard
4. Domingue
5. Subban
6. Ullmark

Then I'd trade Mrazek and Domingue for picks and prospects. Starter goalie would be Fleury, as Pickard plays backup with the hopes that one day Pickard can be a sold starter.

Grubauer is an option to.

I'm going with four. Because I don't think they want the exspensive goalies and should go young. They will probably take someone out of Sweden and and a goalie in the later rounds of the entry draft. I am making Pittsburgh pay me to take Fluery and help them get out of their cap hell and not take Rust. In Arizona I would probably leave Domingue alone and take Burnistrov of Pulkkinen. I would give some thought to Mrazek instead on Raanta and instead take Puemple or Lindberg.
My picks would be
Raanta
Gruebauer
Ullmark
Subban or Bimmngton.

I ended up with four in my list (Fluery, Raanta, Pickard, Wedgewood) because I felt the defensemen available were better trade chips. One weakness of picking more than 3 or 4 goalies is teams you're bargaining with will know that you need to trade the player, since it's not likely you're going to keep more than two goalies at the NHL level. With defensemen, on the other hand, other teams aren't going to know which player (if any) that you want or need to keep, so the bargaining power is on your side.

IMO they take 4:

Fleury
Mrazek
Grubaur
Ranttaa

Fleury, Mrazek, Pickard and Subban.

Fleury - starting goalie
Mrazek - used as a trade chip, not much else to choose from Detroit anyway
Pickard - stays as backup/future starter. Not much else from Colorado either
Subban - AHL goalie, fits in with young mold

And Pickard should be taken over Gruebauer bc a) Colorado doesn't have anything else and b) VGK can then take Schmidt

Taking 4 as well.
1. Fleury
2. Mrazek
3. Pickard
4. Raanta
Can move two of the bottom 3 for decent picks.
Possible 5 is Grubauer, depends on if VGK want Schmidt
Could keep Fleury and Raanta and have a strong 1-2 in goal.

I would take:
Fleury and Raanta to keep
Mrazek to trade for assets
Possible:
I would take Pulkkinen or Richardson over Domingue
I would take Grigorenko over Pickard
Jay Beagle instead of Grubauer