Who should I give my best weapons to?

Solution 1:

I think this depends upon whether you are playing on survival mode or not.

Survival Mode

In survival mode, dweller death is permanent, so you absolutely want to avoid that. Because raider and especially deathclaw attacks can be quite deadly, shutting those down is more important than your explorer spending another hour in the wasteland before you recall them.

Give the best weapons to your vault defenders. Once your first room can kill a pack of deathclaws without stimpacks, then they are strong enough, and you can start giving any extra, awesome weapons to your explorers.

Not

Since you can just revive dwellers with caps, which are so plentiful as to be irrelevant after you get your vault established, incidents really don't matter much. Your whole vault can get wiped out and it's just a hiccup.

On the other hand, most of your good stuff comes from explorers, and the longer they are out there, the better stuff they find. Your whole goal is basically to get explorers out in the wastes as long as possible.

Give the weapons to your explorers.

Solution 2:

In my opinion, having a dweller survive longer in the wild is more important than vault protection because not only can you heal dwellers in your vault during a raid, but you can have up to 200 dwellers in your vault to fight, and raiders, etc. are fairly easy to fight off.
Hope this helps,
-A