AC Milan Vs Liverpool will kick-off on Tue, but the biggest game of the first round of the new league stage will take place on Wed.
Inter is coming to Manchester to take on Man City. Champions of England Vs Champions of Italy - it doesn't get any better than that.
Inter won Serie A last season with a whopping 19 points advantage over AC Milan and made it to the round of 16 in the Chamions League (unexpectedly losing to Atletico on penalties), but bookies don't give them much chances of winning:

Man City very rarely loses at home, so 1 point is probably the most that Inter can hope for.
Wednesday game will be the biggest game because the both clubs are the champions of their domestic league last season. This is the clash of champions from Italy and England. There is a say in my country that when two elephants are fighting, it is the grass that suffers it.
On the other hand, I believe that Manchester city will be able to win Inter because the last time they met was last two seasons finals and City won the match, which gave them their first UCL title in history.