The battle of installation 05 was one the biggest battles but my favorite was the battle of installation 00 or battle of requiem have to be my favorites (mainly because we get the awesomeness of chief and didact) a runner up was the battle of earth
I personally like the fall of reach, and it sure as hell feels like a big battle, thought the maginot sphere battle is of course much larger.
As for coolest, I really like Infinity's second arrival to requiem. Partially because it plows a ship IN TWO, and then deploys a few dozen other ships and hundreds of pellicans. it looks awesome, and I like it.
Biggest battle ever is the battle for the greater ark in the forerunner flood war which dwarf the entire human covenant war I don't know the full size of the battle but the biggest battle of the great schism is the battle of high charity which seen the betrayal of the elites and the infection of the flood on the Capitol of the covenant the biggest battle of the human covenant war is the battle of reach which the covenant fleet was 3 times the size of the fleet that attack earth and the reinforcements that came to aid reach crippled the unsc
Forerunner-Flood War: Battle of the Maginot Sphere. The final battle of the war is arguably the largest in galactic history so far as Mendicant Bias was leading a fleet of 4,802,019 ships of which only 86,436 were warships after the Destruction of the Greater Ark. Meanwhile on the Forerunners side was a grand total of 10,999 ships under the command of Offensive Bias. The Iso-Didact and Offensive Bias knew a conventional victory was impossible against such odds as they were used as a delaying action so the Halo Array could be fired.
Fall of High Charity.
Fall of Reach.
Reach is arguably the largest battle IMO as the Covenant sent over 300 ships against the UNSC's Epsilson Eridani Fleet and as a battle between the UNSC and the Covenant. I'd argue this is the largest battle between Humans and Covenant species, but if we look at the Fall of High Charity at the height of the Great Schism. This has got to be one of the largest battles as the High Charity Defense Fleet was the largest fleet ever seen according to Cortana and for them to split amongst themselves would be one large battle.