Well first off, you need to decide what distances you want to use in a match. The typical long range match here in the states has maximum distances of say 800-1200 yards, though there is an occasional stage in some matches that might exceed that distance. Most matches do not limit your caliber and it’s more typical to have a velocity limit (say 3200 fps or so).
What you will find is that the style and speed of the match and stages typically ends up limiting what calibers get used after a while. For example, in the East of U.S. match locations tend towards faster stage times, say 10-12 rounds from different positions, often on different targets, in 90-105 seconds. Along with the increased use of target impact lights, this lends itself to smaller lighter calibers in heavy rifles.
You’ll see a lot of 6mm cartridges like 6BR, 6x47, 6BRA, 6GT and the like. Even some using .223, .224V, and 22BR. The goal for these competitors is to have a very stable platform with very little recoil so that they can quickly see impacts or misses and therefore get their shots off quicker.
In the Midwest and West, one is likely to see cartridges with more speed, often shooting somewhat high BC, more wind resistant calibers like 6 and 6.5 Creedmoor.
Then there is usually a military caliber category for .223 and .308 that are restricted to maximum weight bullets.
Now, if you plan on shooting matches out to 1 mile, then you’ll find that larger calibers will typically do better there. You likely also use more solid positions and less rifle movement in those stages.
There’s really so much more, but I’d suggest getting together a few that are interested to bounce ideas back and forth and then actually plan a small match. There’s no learning like experience.