Definitely an overall Chapter Adviser, Recruitment Adviser and Financial Adviser as minimum. I believe the CA and RA should be alums. Financial is an area where a non-alum can be very beneficial if there is not a qualified alum to take the position. Make sure that the majority of advisers ARE alums, though. You never want a situation where there's more non-alums than alums working with a chapter. Also, beware of adviser burnout if there are only three advisers! It's a LOT of work!
In a 3 adviser set up, the CA would handle all administrative and programming (and whatever else wasn't covered!), the RA would handle all recruitment along with Public Relations and possibly some New member needs. Financial would be only that, helping manage chapter and house finances as applicable.
After that, I suggest a New Member Adviser (alum), Risk Management Adviser (alum) and Scholarship Adviser. NMA could also oversee the chapter Education program if there isn't a separate adviser for this. RMA is important in this day and age, and often the officer(s) handling this area need adult support! Scholarship can be an alum or not, and is often a good position for a faculty member, which is an added benefit in and of itself!)
"If you want to criticize my methods, fine. But you can keep your snide remarks to yourself. And while you're at it, don't criticize my methods." Rupert Giles, BtVS