In most cases there is no "best person for the job". There's a variety of qualified people (particularly in a system which tends to encourage assigning generalists, as the parliamentary system does, rather than hiring experts). And we've always assigned cabinet posts with things like geography as a factor; the notion that the cabinet should in some respect respect the Canadian population is not a radical one.
As far as the size of the Cabinet, the core ministerial posts are:
1. Prime Minister
2. Minister of Finance
3. Minister of Justice and Attorney General
4. Minister of Foreign Affairs
5. Minister of National Defence
6. Minister of Industry
7. Minister of Transport
8. President of the Treasury Board
9. Minister of the Environment
10. Minister of Public Safety and Emergency Preparedness
11. Minister of International Trade
12. Minister of National Revenue
13. Minister of Veterans Affairs
14. Minister of Natural Resources
15. Minister of Health
16. Minister of Public Works and Government Services
17. Minister of Intergovernmental Affairs & President of the Privy Council
18. Minister for Aboriginal and Northern Affairs
19. Minister of Citizenship and Immigration
20. Minister of Agriculture
21. Minister of Labour
22. Minister of Fisheries and Oceans
23. Minister of Human Resources and Skills Development
24. Minister of Canadian Heritage
25. Minister of International Cooperation
26. Leader of the Government in the House of Commons
27. Chief Government Whip
Sometimes the Chief Whip isn't a minister; you can also have a standalone Deputy PM, or give that on top of another ministerial job, or not use the title at all (Harper didn't; maybe the idea of there being a deputy prime minister offended his controlling tendencies). In the above list there's an odd number of posts, so he'd either have to cut it down by one or balance it out by one. So:
Gentlemen
1. Justin Trudeau (QC)
2. Ralph Goodale (SK)
3. Dominic LeBlanc (NB)
4. Scott Brison (NS)
5. Sean Casey / Wayne Easter (PE)
6. Amarjeet Sohi / Randy Boissonnault (AB)
7. Kent Hehr / Darshan Kang (AB)
8. Marc Garneau (QC)
9. Stephane Dion (QC)
10. Bill Blair (ON)
12. John McCallum (ON)
13. Andrew Leslie (ON)
14. Harjit Sajjan (BC)
Ladies
1. Chrystia Freeland (ON)
2. Judy Foote / Yvonne Jones (NL)
3. Joyce Murray (BC)
4. Jody Wilson-Raybould (BC)
5. Melanie Joly (QC)
6. Carolyn Bennett (ON)
7. Kirsty Duncan (ON)
8. MaryAnn Mihychuk (MB)
9. ?
10. ?
11. ?
12. ?
13. ?
14. ?
The above list covers all the provinces that typically get a single minister. Of the bigger provinces:
- Alberta has two and is probably maxed out, given the lack of female MPs.
- British Columbia has three. It can probably expect at least four; Pamela Goldsmith-Jones and Carla Qualtrough probably being the most obvious choices.
- Quebec has four, including Trudeau himself. A few more can be expected -- probably at least one from outside the city of Montreal.
- Ontario has six, and can obviously expect more than that. Of the ones listed, five are from Toronto/the GTA, the only exception being Leslie, from Ottawa. Expect some to come from other parts of the province, which is likely a boon to people like Bardish Chagger (Waterloo), Maryam Monsef (Peterborough), and Patty Hadju (Thunder Bay).
The above list also omits oft-talked-about individuals like Adam Vaughan, Jim Carr and Bill Morneau. Showing that this is going to require some pretty tough cutting in all circumstances. Or he'll have to create a few more minister of state-type jobs and raise the number above the minimum (which, he can do; the Tories had 40 people in cabinet, they can't criticize).