For me it's 1) free cash flow, 2) capital requirements, 3) other relevant ratios.
Real estate investing is basically buying your next job, so make sure the job is worth it income wise. Free cash flow also has most of your assumptions baked in, stuff like mortgage, interest, taxes, maintenance, vacancies etc. I consider expected improvements as a discounted bonus because I can't count on cashing checks for rent increases I haven't passed yet.
If the free cash flow looks good I'll worry about capital requirements, basically is the deal too big for me to handle. Being short cash and credit when an AC goes out is a giant problem that forces you to make very bad decisions (hard money lender? pay day lender? let the tenant sweat?)
If the deal isn't going to swamp my cash and credit lines and will earn me enough every month to make it worth doing the job, I'll worry about other relevant ratios. Looking at the other ratios will also tell me what other investors are willing to pay. On my 20 unit deal I knew investors were way lower due to CAP rate, so I went in at full price but with an MLO that got her a steady cash flow, no tax penalties for sale, and she got me much better financing than I could ever have come up with anywhere else. Everyone was happy in the end.