A local electrical shop tried to sell me a GE 100 amp transfer switch. My main electrical panel breaker is 125 amps. Would this be ok?
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.
Here's the better way to do a "transfer switch"
A lot of transfer switch products are designed to "bolt on" to your existing panels. They are expensive, add a lot of spaghetti or both. No thanks.
I prefer reliable Tier 1 service equipment suppliers, the kind big companies like Google or Ford use when their power matters. Here we use Siemens.
If you're familiar with normal panel wiring, do you notice how ordinary this is? Every panel on earth is wired like this. It's a plain old subpanel. With one tiny exception: the little blue thing.
Every circuit in your house lands on one breaker, in the normal way you wire things without a gen interlock. Any electrician or trained DIYer will recognize what's going on in these panels. What's more, for circuits that require GFCI and AFCI, you can protect them with one device which will work in both utility and gen modes. (transfer switches can't do that).
To switch to gen, you simply throw both breakers in the top row. You can't miss them, they have the funny interlock/guard on them so you must turn one off before you turn the other on. Boom, now the whole subpanel is on generator. Easy peasy. And the AFCIs still protect.
Let's look at cost.
The little blue thing is Siemens $23 gen interlock which ties two perfectly common $8 Siemens 2-pole breakers so they can't both be on at once. The panel is a Siemens main-lug panel (no main breaker) such as a $87 PL 30/30*. That's it. That's the whole darned thing. Done.
Grand total cost $127. Now what did they want for just the transfer switch?
Or those hokey Reliance spaghetti boxes, what do they cost again? (notice in that photo how there's only 1 neutral wire. That makes them totally incompatible with AFCI/GFCI, so it looks like you won't be using any bathroom or kitchen circuits.)
You will still need breakers ($4 per circuit) unless your existing panel is already Siemens/Murray.
* I can't bear to recommend less than a 30-space panel (remember you lose 4 spaces right at the start) because running out of breaker spaces is a very serious problem so easily avoided when you're buying the panel. A 20-space panel only saves $15, that's $1.50 per regret, I mean space.