In any case, Aquinas's interpretation of the 'whatever is moved is moved by another' principle, as it is unfolded elsewhere in Aquinas's work, doesn't have any problem with persistence in a state of rest or motion: the mover in such a case is (proximately) the nature of the moving object and (remotely) the generator of the nature (or, alternatively, the remover of impediment to motion).
While this is close, on further thought, it isn't quite right. Here's a way to look at it. The First Way is easily shown to be valid. There are only three questions the proof really raises:
(1) Is there really motion?
(2) Is it true that whatever is moved is moved by another?
(3) Is it true that no infinite regress of movers is possible?
If the answer to all three questions is 'yes', the proof is sound. The question we are considering here is (2). Now, it is important to understand what is being asked here. If we find an object in motion, we can ask several sorts of questions, e.g.,
(a) Why is this object in motion at all?
(b) Why is this object continuing to be in motion, given that it already has been in motion?
The inertia principle doesn't quite shed full light on either of these questions. It is, however, part of the answer to (b), since it says that continuing in motion (or at rest) is what objects do, as a general principle (assuming no cause of change). But the second question is actually rather irrelevant to the First Way. The principle that whatever is moved is moved by another is relevant to (a): if it is true, we can ask, what makes this thing to have been in motion? And we can answer a number of things. It may have been wrenched into the motion it has (violent motion); it may have been responding to natural force (natural motion); etc. But the inertia principle doesn't prevent us from asking this sort of question at all. So it doesn't appear that the issue of persistence in locomotion is relevant to the principle at all. (The issue about generators merely points out that Aquinas's argument is not based on the assumption that everything that is currently in motion is currently being moved by some direct cause. It is often incorrectly thought that it does.)
The principle is related to the causal principle that "Everything that begins to be has a cause of its beginning to be"; the latter, in fact, is just a slightly less general form of the principle (if you suppose that there is no motion that has always existed, they are equivalent). This is the relevance of Whewell's analysis; Whewell showed that not only is it reasonable to think the laws of motion are consistent with this latter principle, they can follow from it if you add a supposition or two. I have never seen anyone do an analysis at the level of sophistication at which Whewell does his that suggests otherwise.