I dont think the gaggia baby will cope with that many brews in a short period, the steaming capability will definitely become a bottle neck.
A silvia and sunbeam grinder would be a minimum recommendation. New these will be close to $800. To really churn out the cappas and lattes youd be looking at a hx machine starting at around $1100 + grinder.
Any of the gaggias including the cheaper evolution or carezzza would make the same brew as the baby.
Ive gone from a gaggia baby, *to a silvia to a hx machine and I wont be goiing anywhere for a while yet!
There are many posts in this and other forums discussing these issues. Happy searching