If you want your guitar to stay in tune as best as possible -go Graphtech on the saddles and nut -trust me -I didn't want to believe it for years, but it's true -really true. My guitars flew dozens and dozens of flights this year and before the Graphtech/NYXL setups on all my gig guitars 2 years ago I used to have to acclimate my guitars to the altitude and humidity of the local place as soon as I landed by opeining up the cases and making them soak in the climate to make sure they were not kooky and going out of tune prematurely constantly at gig time. I don't do that at all anymore -as the Graphtech setup allow for a cleaner tension movement across the binding points. NYXL strings are better too for this too BTW. For a live guitar you won't really hear the difference of the softer Graphtech material, in the studio it's slightly mellow but a good Clean Boost with an EQ bump will bring it right back if you want it -or use a studio EQ in the mix phase.
I've had great results as long as they're solid and chrome rather than zinc alloy - pot metal. I'm sure brass or a nice roller could be nice but I don't think it's necessary.
of course the wood has to acclimate -the graphtech nut and saddle makes it easier for the wood to do it's moving versus a bone/brass/plastic nut or anything else
Callaham makes fantastic stuff.
Not the cheapest but damn near the best.
I use and have used generic Fender/squier plate ones, some like in lower picture (can anyone tell whether that looking saddles are chrome or zinc anyway?) and Wilkinson steel ones that I probably like most. And some others.
Plate ones I rarely use in a will of maxing out sustain, but they've all worked. Never had issues with binding and never broken a string.
When speaking of standard ones with height screws, and aside ones made of some soft turd, I even dare to say trem block might make bigger difference.
I dropped saddles in my partscaster on the plate recently due to excessive action. (probably need to shim the neck). Result of removing height screws was the most sustaining strat I've ever played. It's great except I don't quite like the lack of radii in strings.
For me, one of the big concerns is if the screws are going to chew up my hands..or if there are any sharp corners. I am not an aggressive player by any means, but comfort is just as important to me as stability and tone.