Assuming that the last quotation is from Phys.VIII [252b13-252b16]:
Again, we see that a thing that neither is in motion nor contains any motion within itself can be set in motion; e.g. inanimate things that are (whether the whole or some part is in question) not in motion but at rest, are at some moment set in motion; whereas, if motion cannot have a becoming before which it had no being, these things ought to be either always or never in motion."
it seems that the context is the discussion of natutalists' theories [Empedocles, Democritus].
Arisotle is arguing for the "possibility of change"; see [252b10-252b12]:
First, it may be said that no change is eternal; for the nature of all change is such that it proceeds from something to something, so that every change must be bounded by the contraries that mark its course, and no motion can go on to infinity."
Thus, contra Democritus, the finitude of time and cosmos precludes an "eternal rest" as well as an "eternal (inertial) motion", except perhaps the "unaltered" revolution of the celestial spheres.
The Greek tradition regarded Leucippus as the founder of atomism in ancient Greek philosophy. Little is known about him, and his views are hard to distinguish from those of his associate Democritus.
Early Greek atomism is generally taken to have been formulated in response to the Eleatic claim that ‘what is’ must be one and unchanging, because any assertion of differentiation or change within ‘what is’ involves the assertion of ‘what is not,’ an unintelligible concept. [Parmenides' argument] was understood in antiquity to have forced philosophers after him to explain how change is possible without supposing that something comes from ‘what is not,’ i.e. nothing. Aristotle tells us that Leucippus tried to formulate a theory that is consistent with the evidence of the senses that change and motion and a multiplicity of things exists in the world. [...] Leucippus also reportedly accepted the Eleatic Melissus' argument that void is necessary for motion, but took this to be evidence that, since we experience motion, there must be void. Leucippus is reported to hold that the atoms are always in motion (DK 67A18). Aristotle criticizes him for not offering an account that says not only why a particular atom is moving (because it collided with another) but why there is motion at all. Because the atoms are indestructible and unchangeable, their properties presumably stay the same through all time.
The Ancient Atomists extant fragments are few, and many Atomists' thesis are known only through Aristotle's discussion.
We can see also Epicurus and Lucretius.
In particular, De rerum natura, Book 2, discusses the Physical principles of Epicurean atomism.
[Atoms] are in perpetual motion at enormous speed [ ref.II.211-on ], since in the void they get no resistance from the medium, and when they collide they can only be deflected, not halted. Their weight gives them an inherent tendency to move downwards, but collisions can divert those motions in other directions. The result is that, when in a cosmic arrangement, atoms build up complex and relatively stable patterns of motion, which at the macroscopic level appear to us as states of rest or relatively gentle motion. Lucretius compares a flock of sheep on a distant hillside, which appears as a stationary white patch, even though close up the constituent sheep prove to be in motion. The most celebrated part of this account, however, is at II.216–93, where Lucretius maintains that not only to explain how atomic collisions can occur in the first place, but also to account for the evident fact of free will in the animal kingdom, it is necessary to postulate a minimal indeterminacy in the motions of atoms, an unpredictable ‘swerve’ (clinamen) ‘at no fixed place or time’. Otherwise we would all be automata, our motions determined by infinitely extended and unbreakable causal chains.
The key issue is here; without clinamen, atoms move straight down through the void by their own weight. May we say that this is a forerunner of Newtonian Law of inertia ?