Are you buying your hardwood flooringor having it custum milled and installed/ A hardwood installer should take care of any transitions for you.If you purchased wood flooring,the manufacturers have matching trim pieces many of which are T slot mouldings.1/4" can be a bit tight but generally will work.
if you err, err on the larger side up to 3/8".
TIP YOUR TILE MAN, His Retirement plan is not nearly as lucrative as yours and his waning years will be far more painful to boot.
He gives much so you can have a Beautiful Home!!