If you listen to roasters talk about how they approach roasting a new coffee, you might hear about how they cupped a pre-purchase sample and observed interesting flavors. You might hear how measurements of physical properties of that coffee informed the approach they took in terms of where in the roast to apply more or less heat. You might hear various popular roasting theories regurgitated or talk about the general shape of the graph. But there are severe limitations to any of these approaches.
Popular roasting theories become popular because enough people are convinced to try applying one and notice an improvement in the coffee. One thing that most approaches that have been widely adopted over the past several decades have in common is that they'll produce reasonably decent results for enough coffees at a popular roast level. Going from not making a conscious choice about how the roast is approached to any of the approaches described to useful detail in print since the mid-1980's will probably at least help avoid roasting defects. As such, any of these could be a decent starting point, but none of these should be taken as, "the right way to roast." There will be opportunity for improvement with nearly all coffees with any of these basic approaches.
Physical characteristics of the coffee can certainly be helpful for informing an initial approach to roasting a new coffee. Some of these can alert you to potential issues with the coffee. They can give a decent prediction of how the coffee might behave in terms of heat transfer efficiency at different parts of the roast. Physical uniformity or lack thereof can give a sense of how tight a finished product spec might really need to be. You might reasonably use this information to decide to apply more or less heat at different parts of the roast. Tracking this information over time can also be helpful in identifying potential storage issues. Moisture, density, and screen size, however, will not tell you anything detailed about the flavor of the coffee nor will it provide you with any useful clue toward the best finished degree of roast for that coffee.
Cupping a sample roast is a good idea. It will help you identify if there's something wrong with the coffee and it's possible to get an early indication of some of the characteristics that a final product might have, but a standard sample roast is rarely the best way to roast a coffee for use as a finished product. That was never the point of sample roasting. One goal is to be consistent so that the differences among different coffees that are observed on the table are due to differences in the coffee and not differences in how those coffees were roasted, and another is highlighting any defect that the coffee might have. Further constraints on sample roasting protocol might also be adopted to ease communication through a supply chain, especially as it relates to determining if a coffee is an acceptable match to a contract. Some coffees are coincidentally amazing at a sample roast, but most coffees can be improved by doing something different with the roast. Failing to recognize this can result in missed opportunities for some great coffees.
First, it's important to keep in mind that intent matters. Presumably the coffee was purchased to fill a particular role in a product line. That intended use might provide the first constraint on the possibilities that are considered. That's a business decision, but it's one that most roasters need to be aware of in some form.
Taking into consideration what you know about the coffee, how you intend to use the coffee, and experience with similar coffees, try something, but don't just consider a single end point. Try the coffee across a range from where you think the coffee is likely too light to where you think the coffee should be too dark. If you're not sure, don't be afraid to consider a very broad range. For any final degree of roast, you'll never encounter a great example of that roast if you aren't looking for one. Don't forget to record the details of how you roasted this and what all of these different end points are. If you're using Typica, the counting button control was designed for exactly this use case. Taste all of these.
If you do this with every new coffee you consider, you're likely to get good at those initial attempts and will often find how you want to roast the coffee somewhere in that first series, but if you think that there's a better approach available, you don't have to choose a cup from your first attempt. Instead, first identify a narrower range of end points where the coffee was at its best. Then think about what specific characteristics you think could be improved and what sort of change to the roasting plan might bring the desired change in the cup. Roast to your new plan, pull your samples, taste the results. Repeat as needed.
While the trappings of cupping are useful in quickly evaluating several possibilities, remember that this is not the primary way that any of your customers are going to enjoy that coffee. When you've decided on an approach to roasting that you think is right for that coffee, it's important to replicate that roast and then try it prepared in the manner your customers are going to enjoy that coffee. If the results are in line with expectations and you weren't previously constrained with a specific marketing description or product specification, this is also the time to produce those materials. If the results are not in line with expectations, consider why that might be, what changes to the roast might correct the issue, and try again.
If all of this seems too vague and theoretical, I've previously recorded a series called Roast Profile Development in which each episode applies this approach to a specific coffee to illustrate the process over a wide range of coffees and desired flavor profiles. A more basic treatment is in How to Develop a Roast Profile.