Wouldn't the Dave Ramsey method be to walk around with a big envelope full of cash to buy everything? That will be super fun when it comes time to buy a SAN... :-p Seriously, I have no "method", other than to constantly bounce my ideas off of colleagues here (and in citrt Slack), ask what they are paying for this or that, always keeping my eye out for a system/app that could save money or let ministry be done in a more cost saving way.
That said, one of the things I've learned in 11+ years of Church IT is that "saving" doesn't always equate to actual MONEY. Sometimes paying a bit more for something if it saves a bunch of time or labor makes total sense. Being a "good steward" (in my opinion) isn't always about getting the cheapest thing possible, or constructing some system out of "free" OSS software and a cluster of Raspberry PIs that no one but you will ever be able to run or understand. It's doing what MAKES SENSE for your org with the least amount of dollars and/or time, and doing what is common among your peers (free support if you run what your buddy runs, right?). That's my .02.