Yes, there is no question about it, The serial number you posted (0T117804) is considered to be a mariner outboard according to Mercury marines information they have on your engine.
I would think your engine would have had mariner decals at one time. Is the outside of the outboard gray not black in color?
A bigfoot has a bigger gear case housing (Lower Unit) and it supports a bigger propeller for certain types of boats. It normally will works better on most pontoons and a few other style boats. Google "Mercury bigfoot" for more information if needed, Also your service manual should talk a little bit about the bigfoot and non bigfoot as well i believe.
There is information is in your service manual about the prop sizes you can choose to use, It's up to you or a dealer if the boat and engine are new to find a prop that works well for your boat. The most important thing is making sure you top RPM is within specifications. (Your engine is rated for 6000 rpm's)
Hopefully you are using service manual part number 90-828631R3 dated for MARCH 1999 ? If so take a look at page 1A-10. That's the Propeller Information Chart your looking for.
If you don't have the right manual, Here's the section you are looking for, for you to look at.
http://1manual.com/Mercury manuals/Service Manual PDFs/FourStroke/828631r3/1a.pdf
Sorry right now I'm out of time to look up your prop for you, See if your prop's numbers are listed. Good luck.