Use a non-rotating frame centered at the solar system barycenter.
The International Celestial Reference Frame is one such frame. This is more or less a constructible frame. Here we either ignore or account for the acceleration toward the center of the Milky Way, the Andromeda galaxy, and stuff further afield. It does makes sense to ignore those extraneous accelerations; they are very, very tiny, and the variation across the solar system is tinier yet. There's another issue with any such construction. The ICRF almost certainly is rotating. The predecessor of the ICRF, the J2000 frame: Scientists now know it was rotating. The same goes for the predecessor of the J2000 frame, the B1950 frame. In fact, scientists know the ICRF is rotating. The ICRF has been upgraded to ICRF version 2.0. And that too is rotating. Scientists just don't know how much.

Use a non-rotating frame centered at the Earth's center of mass (aka Earth-centered inertial).
Even if the ICRF was perfect, there is no way one can reasonably model the Earth's atmosphere in a computer program from the perspective of such a frame. The length and velocity scales needed to properly model the atmosphere and the length and velocity scales using a solar system barycenter frame just don't match. Oil and water. Even worse, it's a Sesame Street moment! ("One of these things is not like the others, One of these things just doesn't belong.")
The thing that doesn't belong is the solar system barycenter. The only reasonable way to model the Earth's atmosphere is to use an Earth-centered perspective. Now a computer program is starting to have a chance to represent the atmosphere, and do so in a way that is computationally feasible. An Earth-centered frame is accelerating, but we can handle that. We can pretend that $\vec F=m \vec a$ still applies. This result in fictitious tidal accelerations. It's not a problem. Physics still works.

Use an Earth-centered, Earth-fixed reference frame.
A problem remains with the Earth-centered inertial frame described in option #3. The Earth, the atmosphere, and the oceans are rotating, and at different rates. This means that "starting to have a chance" was a bit overoptimistic. It makes much, much more sense to use a frame that rotates with the Earth. This adds even more fictitious forces, the centrifugal and Coriolis forces, but once again, that's not a problem. In fact, this simplifies things to the point where meteorologists do finally have a chance to represent the atmosphere in a way that is computationally feasible.