Check the instruction book for the size of the threads in the router itself. That's what you have to match. As an alternative, take one of the screws out of the base on the router and take it to HD and use their sizing samples to determine the size.
Now, do you mean base plate, or mounting plate. A base plate does not go into a table, it stays on the router and is usually oversized to allow you to have more of the base on the workpiece to reduce chances of tipping.
A mounting plate is made for the table. A quarter inch is rather light for a mounting plate. There's a picture of the a mounting plate below, the one I use on my table which has a few particularly nice features. I have a heavier router so my plate is a Woodpecker brand, thicker aluminum than most plates and with a really convenient twist lock mount for the red inserts. Inserts allow you to minimize open space around the bit for better above table dust removal. I also have a heavier router than the 1617. The Bosch is a great router, btw.
If buy a pre made plate (Kreg has one with the twist lock inserts), the holes will be pre drilled. If you make your own, you can use the base plate on the router with a punch to mark the location of the mounting holes. The second image below is how you should drill your mounting holes. Drill size is a little larger than the thread size. Drill a second hole above it a little larger than the cap on the screw (a short bolt actually). The loose fit allows for small errors in drilling.
The mounting plate will be dropped into an opening you cut undersized, then routed out to the plate size to make a "shelf" on which the plate will fit. There's another discussion of that process at https://www.routerforums.com/guide-b...depth-cut.html
that may be helpful as you set up your table. Do it the ways suggested, not necessarily the way the poster tried to do it.
You can use several pieces of wood to create a simple pattern to follow to hollow out the hole. Double sided tape will hold the pieces down. I suggest you use two layers for your table. The top can be really good, flat ply, the bottom can be a 3/4 thick MDF, glued together.
Welcome to a great hobby. Nothing like it, and lots of help available here as well.