All Buildings at Same Level

Should I level up all my buildings to my headquarters level before upgrading, or push my headquarters first to a high level?

This is to some extend a personal choice, but only in limited way. For Headquarters upgrade there is a prosperity requirement, and you get prosperity points for all building upgrades. For example before you can go to Headquartes 29 you need roughly all your buildings to be minimum 27, few 28. So you cannot lag buildings behind too much.