Depends on your pickups. Vintage types go with tall. More powerful go with short. Me ... I buy both and keep the spare in my case ... They must cost two bucks. Short will always work but if you have OCD like me get both.
This bridge is recommended for carved top bodies only. A neck pocket angle of 1-1/2 to 3 degrees is necessary for best set up. It is difficult to achieve lower action on flat top guitar bodies when using this bridge.
Gee what brand of pups are you looking at and which ones? Or are you winding them yourself? For an LP it doesn't matter if short or long. It only matters if you take them out and put them in a slim body. At least in my experience. Have. You had trouble with other lps? That's why I ask about the make and brand because at the end of the day it's how powerful the bridge pickup is that determines whether you use a tall or short ring.
Like I said, Warmoth sells them both for two dollars, I think. So just get one of each and you'll be good to go regardless of what pick up, whether tall or short legs, you eventually chose.
Still curious about what pups you plan to use.
Generally, Vintage gets tall, high power gets short, medium power depends on your OCD.
Of course, you can always sand down the pickup ring to your perfect height. Dan Erelwine has a video on youtube if you're interested. For me that's too much trouble.