Engineer or Architect?
There are many kinds of engineers and most are specialists like: civil (water, sewer, drainage, etc.); structural; mechanical (plumbing? HVAC, etc.); electrical; acoustical; etc.

Architects know building components like: windows, stairs, doors, roofing, etc. plus they know code issues like required setbacks, energy use (insulation, vapor barriers, etc.). They also know customary construction practices so you don’t get unusual joist spacing, etc. If they need electrical, plumbing, etc. help, let them hire the specialized engineer. 

I’d go with an architect with residential experience. (Some Architects do schools, clinics, etc.) Ask for their resume and a list of references. 

Btw, a residential architect will know a couple good contractors capable of doing the job on time and on budget. (Always get 3 bids for the work.)