I suppose that one should consider the recipient as well. Many of these players are getting up there in age. Can they see as well? Is your sloppy handwriting making it hard for them to read the letter? Is the clean typed letter making it easy? Do they want to read long winder letters citing facts anyone could look up within seconds? I suspect many don't care what the letter says, although some may. A generic letter or form letter would be more likely to turn off a player than a personalized letter I would think. Some players seem to genuinely like the attention and get into it where others churn out signatures like they were serving people at the DMV (Next!). I'd love to hear what Bobby Doerr really thinks about all the requests he gets, the real uncensored truth! He gets a lot I am sure and turns them around fast! Does he really enjoy it? Does it feel like it's an obligation? Something in between? It has to take up a fair amount of his time, time that he doesn't have too terribly much left of being in his 90s. I don't know if he'd ever share his true feelings, but it would be interesting none the less. I'm guessing he truly enjoys it, but who knows for sure.
I have only sent a few out, less than a dozen, and I have written them by hand. I generally ask for a signature, explain why I am sending (I collect Dodgers, for example) and thank them. If there is a small fact or tidbit that is relevant and meaningful, then I might use it. I sent Willie Wells a postcard of my submarine, mentioned my service and thanked him for his service for example, as we both had military service. Not sure what he thought, but the PC didn't come back with my request.
There is no magic answer to this. Do what seems right and it may involve differences at times.