So, trying to estimate our iron needs. We're receiving 150 tons, and about 100 tons of that is reserved for the legion.
The figure for the night's watch we received was about 1200 men, and from canon it seems roughly half are stationed at castle black (600), with 150 of them rangers.
That gives us a rough figure of 300 rangers, and 900 builders and stewards for the whole watch. Looking over their roster, I'd be surprised if they had more than 2 dozen knights who knew how to properly wear fullplate. Double that and give them 50 suits of full plate should see to that aspect for a good long while.
All the members of the Night's Watch are trained to fight, but the level of training is going to vary pretty widely. For rough calculation, I'll just be going with a Breastplate for each member, with the difference between chain shirts and reinforced breastplate canceling each other out.
I'll go with 900 light shields, and 900 heavy shields. Enough that everyone should have exactly what they prefer, depending on the situation. A ranger might need to keep armor penalty down when ranging, but want a heavy shield if defending the wall itself, for example.
So it should be roughly about 29 tons of steel to armor the full night's watch (18 tons regular, a bit over a ton for full plate, and just under 10 tons for the shields).
Another 3 tons gives each man a longsword and a dagger, giving us a running total of 32 tons (added obsidian arrowheads and spearheads are very cheap for us to produce, and don't need steel so aren't included). We could add three tons of tools, nails and misc. and call it 35 tons for the watch, leaving us a reserve of 15-35 tons, depending on how many legionnaires we recruit (or another 375-875 legionnaires Post-Tyrosh. Or more importantly, about 667-1555 out of 2000 for a watch force, which is what we're going to be rushing immediately after Tyrosh.)
I think this leaves us in a good position. Enough steel to have our legion ready for Tyrosh, equip the Night's watch with steel arms and armor, and have enough steel that I think we can get the rest for the first Watch garrison via melting down captured weapons and armor from Tyrosh.
In summary:
80-100 tons for the legion
35 tons for Nights watch
15-35 tons for watch garrison.