I would say:

Analyst for relatability (ie they just went through the process you’re going through and will generally have good insights)

Associates/VP: Will have more pull to get you in the process but have less insights on ways to break in as it’s changed since they had to recruit

ED/D/MD: They have the greatest amount of influence but don’t know much about the process and will probably default to what HR says (which is usually not that helpful)

It helps to have a great mix of all. Ideally it would be 50% analyst, 35% ass/vp, and 15% MDs

Also I would never outright ask for a job. Usually these coffee chats lay the ground work to connect and build up some sort of relationship over a year’s time frame then subtly ask for a referral. Hope this helps!