How should have have handled Confederate aggression?
It is easy to criticize Lincoln in hindsight, because it is 160 years later, and the Lincoln Presidency was months old.
However, the way Fort Sumter was handled by both the Buchanan administration and Lincoln administration was the worst way it could possibly be handled.
The Buchanan administration allowed Secessionists/Confederates to seize weapons and forts. Buchanan made an agreement with South Carolina Governor Higgins to not reinforce Fort Sumter in return for the Confederates leaving it alone. And he attempted to reinforce it multiple times, his only action to prevent secession.
What Lincoln should have done... Is not follow in Buchanan's footsteps.
Virginia had a vote on secession, and secession lost but it was a close vote. Lincolns primary objective should have been to secure Virginia. Lincoln indicated this when he gave a public statement that he would "trade Fort Sumter for Virginia not seceding".
Likewise, Davis was trying to provoke a reaction at Fort Sumter to dog Virginia into seceding.
Instead, Lincoln decided to send a flotilla filled with weapons and soldiers to resupply and reinforce Fort Sumter and fire back at Confederate batteries. This provoked Davis into giving the order to fire on Fort Sumter, but it also provoked Virginia into seceding. In hindsight, a bad more.
Fort Sumter was both David and Lincoln provoking one another into war so they can go back to their base and justify a war. And it worked out better for Davis because he got extra and significant states.
Lincoln had an endless number of ways on where and how he wished to deal with the Confederates. Davis was limited as he was riding on public outcry to provoke secession and win states. The way Lincoln chose cost him key states which prolonged the war for years...