With which units can he be played?
Proberly the best way to play Sulla is with infantry and artillery, or both at the same time.
What is his playstyle?/How to play him?
Sulla should be seen a bit as a defensive commander with the ablity to use artillery, guarded by Roman legions.
An offensive can be a harder to pull of but rewarding.
Tips and tricks
Use Fortify with legionaries while running out on the enemy flanks with javelins.
You can block of a narrow path with Fortify while hitting the enemy with artillery.
Don't use Proscription on all your units if they all fight in the same location. Try to see if only one is enough to debuff your enemies.
If you play with a mix of javelins and infantry, use Proscription on your javelins rather than on your infantry: your infantry won't be debuffed and will hence be more effective in melee.
Lucius Cornelius Sulla was born into a dishonoured patrician family in 138 BC in Rome.
Though his father died then Sulla was in his teens he was no less well-educated and fluent in Greek, a sign of a proper patrician education. With money from his step-mother and an older lover, he managed to move in higher social circles and become quaestor to the consul Gaius Marius. As Marius led Roman troops against the Jugurtha armies, Sulla followed and turned out to be an able military leader which Marius envy him.
Sulla served with distinction doing the Social Wars, 91-88 BC, and led his men to victory at Aeclanum. Marius knew the glory would befall the one who was victorious and then Sulla won the war, the rift that had grown slowly since the earlier years only grew larger.
Sulla had become a popular consul and war hero when war broke out in Greece. Mithridates VI had rebelled and just as the Social Wars the victorious general would be hailed as a hero of Rome. The Senate chose Sulla to lead the armies of Rome but Marius wanted the glory to finish out his career, so Marius and the statesman Sulpicius conspired and succeed in getting the Senate to give Marius the honour. When Sulla got this news he turned around and marched, with six legions, at Rome. After he had taken Rome he declared Marius, Sulpicius and their supporters enemies of the state. Marius was able to flee but one of Sulpicius' slaves betrayed him and got executed. Sulla gave the slaves his freedom as thanks but was put to the sword right after for having betrayed his master.
Sulla was now able to deal with Mithridates rebellion and took Athens but he found out his enemies organized against him back home, he once more marched on Rome. In 82 BC Sulla defeated his opponents in battle outside of Rome and became master of Rome. The Senate was forced to declare him dictator and his reign of terror began.
He made a policy of proscription where people who were considered the enemy of the state was denounced and executed. Though some of these people were sympathetic to Marius, most were not and just killed so their estates could be taken and sold to add to Sulla's wealth. It's estimated that up to 9.000 upper-class Romans were killed during this policy.
His important reforms to government which would increase the senate's power and lower the risk of future problems but the good he did are overshadowed but the unreasonable proscriptions.
Sulla died in 78 BC, either from liver disease or a ruptured ulcer after years of alcohol abuse and yet in his failing as dictator, he was given a hero's funeral.