Zac,
I'm surprised to say that I have never really given that question a lot of thought, perhaps falling in the camp of others that they have to fit the entirety of the hole, course, and landscape. Green design must simultaneously fit the needs of 4 very different golf shots - the approach shot, potential short game recovery shots, first putts, and second putts. I don't figure I need to give so much attention to third putts, although some here seem to advocate for greens that cause these often, LOL.
And, I tend to address those issues in about that order, i.e. approach shot first.
Also, it depends on the type of course to a degree. But, one of my biggest influences on this is Pete and Alice Dye, who pointed out to me that average golfers like gently rolling greens throughout, and the combo of approach shot and daily pin location most naturally contribute to a different putt every time they play. They thought pros preferred flatter greens, because they only had a few days to learn them before a tournament each year.
I also have some thoughts based on co-designing with pros.
After talking to Lanny Wadkins, I prefer to limit multi-tier greens to a maximum of 4 (if he said it, I will go with it)
Talking with Jack Nicklaus, he likes a two tier green (narrower at the back) on long downwind par 4 holes, which he said are about the only type hole he would consider running a shot in with less spin, so I usually find the longest downwind par 4 and put that kind of green there to start. For the longest par 3, 4, and 5, I tend to use smaller greens across the line of play, but without a lot of frontal bunkering (see just below)
Larry Nelson and Notah Begay III preferred medium par 5 holes have at least a narrow opening where they, as shorter hitters, could use their accuracy to reach the green with 3 Wood, negating some who can fly a high iron in and carry hazards.
All of them seemed to like rolling edges and a flatter middle, with the ridges edging in to protect corner pin positions, while aiming at the middle was pretty safe. Again, there can be a few exceptions, and a few here think those exceptions ought to occur every other hole......
In short, as often as I can, I prefer to:
Set the green to about the size as a minimum, the USGA Slope system has suggested is required for 2/3 of average golfers, and allow one difficult, tucked pin to allow a set up to challenge better golfers, sized at about 10% x 10% width and depth of their approach shot.
I like to set the green angle with the wind, to help players craft a shot, not defeat them. If I can't, I tend to go with wider greens. I tend to put the Sunday pin also aligned with the wind, i.e., downwind and right gets the Sunday pin in the back right of the green, or anywhere right, but hardly ever front left in that wind. Headwinds tend to get shallower greens than typically downwind approach shots, which are deeper to account for less spin.
Someone also mentioned variety, which is what I conceptually strive for, and why I am generally against waiting until you are on sited to start figuring out what you want to do. It sounds odd, but to me, knowing we are all creatures of habit, i.e., Sh*T, shower, shave in the same order every day, I think consciously planning variety by features creates variety more than winging it, because, in reality, you aren't bringing radical new ideas every day you are out in the sun (and if you are, maybe you should hydrate!)
I address green designs on a plan, before construction, striving for 1-3 very small greens, at least 2 very large ones, perhaps one very wide and one very long, and a conscious variety of "normal" size greens bending left and right, with maybe 2-4 strongly across the line of play (after hearing critiques of Nicklaus greens angling hard right for too long). I know that greens appear to angle more strongly at ground level than in plan view, and any green angled more than 30 degrees basically appears as almost 90 degrees, so on plans, I am biased towards keeping the angles to the line of play low, i.e., 5 to 20 degrees right or left, on the plan, unless it is one of the 2-4 I want across the line of play.
I am not against using templates a few times per course, i.e., Redan, Biriattz, Short, Double Plateau, although I don't force them in there, unless the topo suggests them (or, it's dead flat and the green must be created.) Not am I against using any other less famous green as a base model if, in my mind, the contours and setting are similar.
Once contouring greens, I strive for some flatter and some more rolling (purposely drawing a grading plan of one green at 1.75% base slope, and others at 2%, 2.5% and maybe even 3% depending on the hole, wind, uphill or downhill approach shot, etc. But, the point is to not allow the golfer to read the green based on the others, since all have more or less severe contour.
As your first design, you won't have this problem, but I also leave 2 to 3 greens to try something I have never tried before! The discussions here focus so much on the unusual, but I have found that golfers will tolerate "non standard" greens (reverse slope, overly rolling, etc., a few times per round, but over doing any of them causes most to consider the course just goofy golf.
Anyway, I'm sure I take many more basic ideas into designing any particular green set, and might make exceptions on a truly different site. And, as always, just MMO. Yours may vary....heck, sometimes even mine varies, LOL.