Is there a preferred sequence for buying upgrades in the armory?
Solution 1:
Okay, lame answer time.
The point of the campaign upgrade system is that the choice is yours to make. The developers have stated that they want you to play through the game multiple times, playing the missions in different orders, trying different research, getting different armory upgrades. So there is no correct answer for the "preferred sequence" - making different choices will give you a different experience, and a part of the fun is talking with your friends about how you did it differently and trying something else on a later playthrough.
Myself, I picked up enhanced Medics healing speed, increased armor, upped Bunker health, and Perdition Turrets to keep my base defenses alive and well without much assistance. Then I upgraded my Reapers to go on entertaining adventures with my super-mobile special ops reaper brigade, and am having a blast with it.
None of the upgrades I have seen so far look useless. The only wrong decisions you can make are buying upgrades and then never using them - don't enhance your Marauders but then build only Marines - and not buying anything at all.
Solution 2:
Warning: This is clearly subjective.
For most early missions of the game, even on brutal, all you really need are the marine and medic upgrades. Marines and medics cost very little and have a lot of staying power against most enemy units.