100 amp transfer switch for 125 amp home
No, you can't do that

A 100A manual transfer panel has a 100A breaker for the utility-side input; as a result, it would be a "bottleneck" if you put it inline with your service, restricting the whole service to 100A. However, this does not mean that you have the wrong transfer switch, so do not go running back to the store before you read the rest of this answer!

But, you probably don't want to transfer the entire house

Whole-house transfer sounds good at first, but especially for folks with smaller generators, its not nearly as good a plan in practice as it is in theory.  Many of your larger loads, even on a smaller service, are rather large for a generator, and are not nearly as important to have on a generator unless you are dealing with a situation where the power regularly goes out for days on end.  (Do you really need your dryer on a generator, or your range for that matter?)  Furthermore, you will have to flip a zillion breakers in order to not overload the generator when you transfer to generator power -- probably not the easiest thing to do in the dark!

As a result, what I would do is put a 30A, 2-pole branch breaker in the main panel to provide the utility-mains-side feed to the transfer switch, and then put a subpanel in off the standby side that only has breakers in it for the critical loads -- the ability to have heat so the house doesn't freeze (with a 125A service, I can tell you do not have electric resistance heat), the ability to run a small cooking appliance (such as a plug-in electric griddle or a microwave), your refrigerator (if it's not on the aforementioned small appliance branch circuit, that is), 1-2 circuits for standby lighting + the smoke alarms and selected receptacles, and perhaps the ability to run the hot water heater as well (an electric tank-type heater can be half-volted for use on a generator at the cost of very slow recovery, as well as an extra transfer switch and some clever wiring), as well as any sump or well pumps the house may have.