There are comprehensive online calculators for determining the required force to turn any given screw+nut pitch to lift your load. Many likewise allow you to account for gear reduction. But that calculation is too welll implied to require explanation. Better vendors provide these tools. You can also acquire the industry-standard formulae, as I have, and build your own calculator in the format of a spreadsheet. The general pattern of my own practice is to compare several motor candidates at once, thus to record permanent instances of the determining parameters. I have attached an example, which you may adapt to your purposes.

However there are further issues you are concerned with. The choice between open and closed loop motors for example will determine how much heat and noise you will generate and how much energy you will consume. The more typical open loop motors will exert the most energy and generate the most heat while simply sustaining a position. Similarly, they tend to generate more noise and vibration while stepping between positions.

Conversely, you may generate more power and less heat per consumed energy with the more recent innovations of closed loop motors. These advantages require different drivers and different software code. But hardly increase initial costs at all. So you definitely want to read up on the differences, because long term costs are greater for the less-expensive open loop designs; and your initial setup will deprecate drivers and software code if you reach for the advantages of closed loop motors sometime downstream. The information your decisions depend upon is everywhere.

You also want to decide whether it might be more advisable to deliver upon your movement objectives with a pre-built linear actuator type stepper, of which there are both captive and non-captive types. The effective nut and related mechanisms you desire, are built into these assembles. Most commercially available implementations are relatively delicate. But more massive implementations do exist.

To make some attempt to point you in the right direction then, you should first search for the terms I have used. I suspect that if you can find a closed-loop motor type of the kind you eventually discover to want most, then you will opt for the closed loop type. If this is available in any commercial linear actuator that will be ideal for your purposes, then obviously, you will go with the pre-built linear actuator, because it will eliminate much of the responsibilities and costs of designing and fabricating yourself, some similar such componentry. Often I have responded to specific design objectives by formulating an ideal design, which, only upon much further reflection, I find I can more readily resolve with a commercial actuator. Do not despair if you find yourself running this course. It's practically inevitable.