Below is a partial list of Engagements the Stafford family were involved in.
Cades Rebellion

Shrewsbury 1403

Edmund, 5th Earl of Stafford, commanded vanguard of Henry IV's army against Harry Hotspur and was killed during the battle.

1st Battle of St. Alban's, 22nd May 1455

Humphrey, 1st Duke of Buckingham, commander-in-chief of the Lancastrian forces for Henry VI. Fought with his son, Humphrey Earl of Stafford, was wounded defending the King but both were spared after being defeated.

Ludford Bridge

Humphrey, Duke of Buckingham also fought here in support of the King.

The Battle of Northampton, 10th July 1460

Humphrey, Duke of Buckingham, commanding the Lancastrian force in a defensive position with it's back to the river Nene. Due to the betrayal of Lord Grey the Yorkist's are victorious and the Duke is killed defending the king.
Humphrey Stafford, future Yorkist Earl of Devon and part of the Southwick branch was apparently present on the side of the Yorkists.
Also some conjecture as to the presence of one John Stafford, who is recorded as slaying one Sir William Lucy after the Battle.

The Battle of Mortimer's Cross, 2nd February 1461

The aforementioned had accompanied Edward, Earl of March from South Wales, where they had been busy recruiting men. Fought on the Yorkist side and was victorious.

The Battle of Towton, 29th March 1461

Since the Duke of Buckingham was currently in a minority and ward of the King, owing to the death of his father in 1457 and grandfather at Northampton in 1460, Stafford participation was minimal after this point. However, as a ward of the King, Henry VI could summon Stafford troops on his behalf. So it is possible some fought at Towton on the Lancastrian side, ultimately losing.
Once again, Humphrey Stafford of Southwick supported Edward and was rewarded with the title Lord Stafford of Southwick.

The Battle of Edgecote Moor, 26th July 1469