To best maximize your time before the gates open, doing multiple things while using spells with cast times is in your (and your team's) best interest.
For 2v2, I usually do the following:
Start casting Imp. (Yes, imp.) Imp completes.
Start casting a spellstone.
While spellstone is finishing up, buff yourself and your partner with fire shield.
Start casting a healthstone, while equipping your spellstone.
Start casting a voidwalker, while trading your healthstone to your partner.
When the voidwalker is complete, start casting another healthstone.
Take the time while this healthstone is completing to target your partner.
Cast unending breath and detect invisibility on your partner.
Cast unending breath, detect invisibility, and sense demons on yourself.
You will usually complete this series with ~30 seconds left to go until the arena starts if done correctly.
With 15 seconds left to go until the gates open, cast shadow ward.
With 13 seconds left to go until the gates open, sac your voidwalker and begin casting a felhunter (or the pet of your choice).
This will give you a nice shield 17 seconds into the battle.
If you don't have master summoner, start casting your pet of choice and after 5 seconds your voidwalker will be able to be sacced.
I would not recommend doing this with master summoner, as sometimes it grays out your pet bar and you cannot use the abilities (even attack, follow, or stay) of your new demon.
For 3v3 and 5v5: Don't worry about the voidwalker shield, it eats up too much time, and your Felguard or desired pet will not recieve the buffs it needs.