When writing an electron configuration for a transition metal, what is the last orbital type to be filled - an s, p, d or f orbital?

It would be d.

Reason being said ...

the electron configuration normally goes like this ...

1s2 2s2 2p6 3s2 3p6 4s2 ...

until you hit the transition metals ... remember those have a special rule ...

even though you are in the 4 sublevels for the orbitals ... it goes down 1

Making it 3d ... (1,2,3,4,5,6,7,8,9,10)

Going on ...

at 5s2 then, 4d1, 4d2, 4d3, 4d4, etc ...

at 6s2 then, 5d1, 6d2, 6d3, 6d4, etc ...

Thus, D orbital is your answer.