Hi Mark! Welcome to the forum!
It’s a huge subject! Mandolins & guitars can be similarly affected in tone by which woods are used in construction.
If the selling point is simply unidentified “solid wood” it probably means it’s not plastic. or plywood. It is a typical “selling point” of inexpensive instruments. (Yes, a “few hundred dollars” is relatively inexpensive for instruments).
Here is a link to a very basic discussion that might bring some start to understanding.
I’d suggest calling the guys at Ben’s store to talk over options they maybe could provide. At the least you can be confident you will get the truth and a fair shake, and they can help steer you in the right direction. They are very knowledgeable on the products they offer, as well as instruments in general…
Hope this helps, have a great day.
Dave