John West wrote:

We should get a translation of the original up, too. Aquinas's summary is better than Weingartner with (4).

At your request:

Latin wrote:

Prima autem et manifestior via est, quae sumitur ex parte motus.

Certum est enim, et sensu constat, aliqua moveri in hoc mundo. Omne autem quod movetur, ab alio movetur. Nihil enim movetur, nisi secundum quod est in potentia ad illud ad quod movetur, movet autem aliquid secundum quod est actu. Movere enim nihil aliud est quam educere aliquid de potentia in actum, de potentia autem non potest aliquid reduci in actum, nisi per aliquod ens in actu, sicut calidum in actu, ut ignis, facit lignum, quod est calidum in potentia, esse actu calidum, et per hoc movet et alterat ipsum. Non autem est possibile ut idem sit simul in actu et potentia secundum idem, sed solum secundum diversa, quod enim est calidum in actu, non potest simul esse calidum in potentia, sed est simul frigidum in potentia. Impossibile est ergo quod, secundum idem et eodem modo, aliquid sit movens et motum, vel quod moveat seipsum. Omne ergo quod movetur, oportet ab alio moveri.

Si ergo id a quo movetur, moveatur, oportet et ipsum ab alio moveri et illud ab alio. Hic autem non est procedere in infinitum, quia sic non esset aliquod primum movens; et per consequens nec aliquod aliud movens, quia moventia secunda non movent nisi per hoc quod sunt mota a primo movente, sicut baculus non movet nisi per hoc quod est motus a manu. Ergo necesse est devenire ad aliquod primum movens, quod a nullo movetur,

et hoc omnes intelligunt Deum.

English wrote:

The first and clearest way is that taken from movement or change (ex parte motus):

It is certain, and obvious to the senses, that in this world some things are moved. But everything that is moved is moved by another. For nothing is moved except insofar as it is in potentiality with respect to that actuality toward which it is moved, whereas something effects movement insofar as it is in actuality in a relevant respect. After all, to effect movement (movere) is just to lead something from potentiality into actuality. But a thing cannot be led from potentiality into actuality except through some being that is in actuality in a relevant respect; for example, something that is hot in actuality—say, a fire—makes a piece of wood, which is hot in potentiality, to be hot in actuality, and it thereby moves and alters the piece of wood. But it is impossible for something to be simultaneously in potentiality and in actuality with respect to same thing; rather, it can be in potentiality and in actuality only with respect to different things. For what is hot in actuality cannot simultaneously be hot in potentiality; rather, it is cold in potentiality. Therefore, it is impossible that something should be both mover and moved in the same way and with respect to the same thing, or, in other words, that something should move itself. Therefore, everything that is moved must be moved by another.

If, then, that by which something is moved is itself moved, then it, too, must be moved by another, and that other by still another. But this does not go on to infinity. For if it did, then there would not be any first mover and, as a result, none of the others would effect movement, either. For secondary movers effect movement only because they are being moved by a first mover, just as a stick does not effect movement except because it is being moved by a hand. Therefore, one has to arrive at some first mover that is not being moved by anything.

And this is what everyone takes to be a God.

Chop "in that respect" off the end of (4), and I think you have the right reading of Aquinas. (I mentioned Weingartner because he's the only author I know of who has the First Way in the original, an attempt to rearrange the original into premises and conclusions, and in the boiled down symbolic form Daniel asked for, not because I stand behind everything he writes about the Ways.)

Does Kant's critique of Aquinas's cosmological argument where we go from empircal evidence (such as causality) to non-emprical suggestion such as existence of God be a good critique?

What I've had a hard time understanding as long as I've been looking into the first way is, why do we need a single first mover that is pure actuality rather than a universe full of stuff that is partly actual and partly potential all actualizing the potentialities in each other into the past?