Hello. What is your question?
You want a new beam to span the full 17’-9” and need calculations on paper? I can provide the size for this question and I can provide the detailed calculations as an additional service. I will submit the additional service offer for you to consider. If you accept it, I will provide the detailed calculations for bending, shear, and deflection within 3 hours of accepting the offer and providing any additional information I need.
In terms of what? The size? It won't be a report; it will be detailed calculations.
An LVL will be large. A steel beam will be smaller.
A 7" x 16" 2.0E LVL will just barely work for deflection for a floor without ceramic tile. This assumes you're in a region with snow loads less than 25 psf.