In general, I would vote strongly for installing a locker before opening the t-case. As others have said, being locked--even in just one axle--is probably the single biggest increase in capability for nearly any 4x4. Two lockers are better than one, of course, but the increase in capability going from one locker to two is far less than the increase in capability going from open/open to one locker.
I never would have thought to lock the front first, good info guys.
In
select situations, it can be an acceptable move. For example, on a TJ with the rear Dana35c it is best to avoid locking the rear since it's already a ticking time bomb and any extra stress is just asking for trouble.
As another example, let's say you want to re-gear your axles down the road but you cannot afford to do that right now
and install your locker. Furthermore, let's say re-gearing would require buying a new carrier for the rear axle but not the front. In this case, locking the front first means you could re-use your locker after you re-gear... whereas locking the rear would require you to buy a new locker when you re-gear.
Having said all that, I still feel that it is best to lock the tail first unless there is an exceptional reason like those I just listed. Why? Because a locker seems to be more beneficial when
climbing than when descending... and when you're climbing, you'll be transferring a
lot of your rig's weight to the rear tires. When your front tires are mostly unloaded weight-wise, it doesn't much matter if you're turning one of them or both of them. Why not send your torque where it is needed most?