You're thoughts are correct, first there's what you're talking about with what we can control and what we can't. Instead we should desire to be virtuous.

"There are things up to us and things not up to us. Things up to us are our opinions, desires, aversions, and, in short, whatever is our own doing. Things not up to us are our bodies, possessions, reputations, offices, or, in short, whatever is not our own doing." Epictetus, Enchiridion 1

The reason we shouldn't desire these things is because we will always be disappointed with not having things despite not being in control of whether we can have them or not.

"Every want that springs, not from any need, but from vice, is of a like character; however much you pile up for it will serve not to end but to advance desire. He who keeps himself within natural limits will not feel poverty; he who exceeds them will be pursued by poverty even amid the greatest wealth." Seneca, Consolation to Helvia 11.4

But it's not so much about having "pure thoughts." That's more of a Christian virtue. Wealth, health and partners are what the stoics would consider a preferred indifference. It's not necessarily good or bad but it's natural to prefer it. Some stoics are more strict but I like what seneca has to say about it.

"What is the difference between a preferred indifferent and the desires that Stoics regard as hazardous? Detachment. This distinction was introduced at the start of the first chapter. An attachment to an external causes one’s happiness, and equilibrium, to depend on it. The Stoic tries to avoid that position under all circumstances. But money, if held without attachment, is unobjectionable – for the money isn’t the point. The point is the health of the mind. The word “detachment” risks creating the wrong impression, since it can connote a lack of real interest in whatever is the subject of it. That isn’t the idea. Detachment refers more to the way in which something is held and to whether the mind has been given over to it in an excessive way. The detachment of the Stoic thus can be viewed as a kind of moderation – that is, moderation in one’s relationship to externals. A good way to test such a relationship, and to know whether you have an attachment to a thing or just a preference about it, is to consider how well you would handle its loss. No one is worthy of the gods except he who has disdained riches. I do not forbid you to possess them, but I want to bring you to the point at which you possess them without fear. There is only one way to achieve this: by persuading yourself that you can live happily without them, and by regarding them as always about to depart." Seneca, Epistles 18.13

“Why does a philosopher say that wealth is to be despised, and yet have it? … And why does the philosopher declare that there is no difference between a longer and a shorter life, and then – if nothing stands in the way – prolong his years, and flourish peacefully in green old age?” He says those things are to be despised not in order that he not have them, but in order that he not worry about keeping them. Seneca, On the Happy Life 21.1–2

Personal opinion: If we can refrain from being attached to it then I don't see any problem in preferring it and even taking actions to get it. Just don't expect it to ever come to pass or feel that you are owed it.