Army Commander: U.S. Grant
I Corps: James Longstreet
II Corps: John Reynolds
III Corps: Winfield Scott Hancock
Cavalry: John Buford
Artillery: Henry Hunt
Chief of Staff Dan Butterfield
Intelligence: George Sharpe
Logistics: Montgomery Meigs
Engineer: Edward Wellman Serrell
Medical: Jonathan Letterman
Grant is the best Commander of the era because he understands both strength and limitations, making the best use of the Subordinate Officers and units under his command.
He issued Clear & Consise Orders, informed by his understanding of capabilities.
He had the Grit to fight, and keep on fighting. Of course he made mistakes, but he had the wisdom to learn from them.
Longstreet is one of the best Generals of the ACW, he understands the advantages of the Defense, and the merits of entrenching. He is capable of conducting prompt counter attacks, as well as deliberate assaults.
He and Grant had a great relationship before and after the war. Grant married one of Longstreet's Cousins, and Longstreet stood up for Grant.
Reynolds has a proven record as a Corps (and "Wing") Commander, he refused command of the Army of the Patomic, because he would have been micro-managed by Henry Halleck. Reynolds had been Instructor of Tactics at West Point just before the war; and proved he could apply good tactics in Combat. He also had a good sense of Terrain.
Hancock was vital to the victory at Gettysburg, late on the 1st, and preparing Cemetery Hill for the defence resulting in victory. Competent at Offense, Defense, Maneuver, Training and Logistics.
I strongly considered Thomas "Stonewall" Jackson, he is the Hammer to Longstreet's "Anvil" however, he did not always work well with others. Still, if I had a IV Corps, I would choose T. Jackson to command it.
John Buford knew it was best for ACW Cavalry to fight Dismounted. More importantly he understands Key Terrain, and how it could be used by Infantry and Artillery, as well as Cavalry.
He Communicated Clearly to subordinates and Superiors. Reconissance is of little value if it is not Quickly and Accurately Communicated to Those Who Need It!
Hunt wrote the Manual on the use of Artillery. He was a good Trainer, and a good Combat Leader. Union Artillery was considered the most competent Branch.
Dan Butterfield has some moral faults, and was a partisan of Hooker, undermining Meade, and others, but I think he could have worked well with Grant. He contributed to the impovements to the AoP with Hooker.
The other supporting branch leadership are not contrivercial, I think.