Power: Electric houses just need a lot
Generally speaking, all-electric houses get 200A, 320A or 400A service. Now you are adding a second dwelling that's also all-electric. So we can definitely disqualify 200A (for both) as inadequate.
Therefore your best bet is a 400A meter-main. Even if the power company won't provision that much, they could upgrade the service later if your usage warrants it.
The size of the main breakers will be decided by the power company.
Subpanels: Think big
As for the subpanels, **the single most important thing about panels is to provision enough spaces. 40 spaces per panel is not too many, especially in an all-electric house where many loads will be 240V and gobble up 2 panel spaces. 30 spaces is a bare minimum that will likely cause you trouble later, but it may be suitable for the auxiliary dwelling. Given the small cost to upgrade to a 40-space, there's no reason to paint yourself into a corner.
We certainly do not want you back here later going "my panel is full, how do I add this breaker?"
And double especially, don't make the most common mistake I see: chintzing out on the panels, and then spending a fortune on copper wire when aluminum is the right stuff, and 1/3 the price.
You may be accustomed to using "double-stuff" breakers to economize on spaces. These are no longer practical, due to the need for almost every breaker to be AFCI or dual mode AFCI/GFCI. These are not made in double-stuffs.
You mentioned a 125A subpanel, and that will surely be much too small in terms of numbers of spaces. The subpanels can be any size you please; that is merely a current limit for the buses and it doesn't need to match the official main breaker in the meter-main.
If the subpanel has its own main breaker, there's no need for it to match either. So you can feed a 225A subpanel from a 125A or 200A main - no trouble at all. The panel in the house doesn't even need a main breaker since it's in the same building as the meter-main. If it's not attached (e.g. via a breezeway), the auxiliary dwelling would need a "main breaker"; actually what it needs is a main disconnect switch, but using a "main breaker panel" is usually the cheapest way to do that.