#1 Carlo Ancelotti

There are very few managers who boast a CV like the Italian. He has Premier Leauge experience with Chelsea helping them win the Premier League and FA Cup. He has also won trophies with Juventus, AC Milan, PSG, Real Madrid and Bayern Munich.
He is also a very successful manager in Europe as well winning Champions League with Milan and Real Madrid.
Under Ancelotti, Arsenal are likely to play a 4-3-3 free-flowing fluid attacking football. His Italian roots will make sure that Arsenal builds from the back and they have a strong defence.
He is currently unemployed and living in London so it should very easy for the Gunners to sign him as well. Overall he should be a good fit for them and the legacy of Arsene Wenger will be in safe hands.