Pellet weights

If you are considering a true 10 M Olympic style rifle, they are all .177, and I think tuned to shoot a 7-8 grain pellet around 550-580 fps. I believe they mostly use wadcutter style pellets, and I'm sure that testing different pellets is the standard process. It is a specialized and demanding sport. If 10 meters is simply the distance at which you'll be shooting, but with a more general purpose rifle, then your choices are unlimited. And yes, lower power and lighter pellets will probably br best. I would suggest one of the 12 fpe rifles that are the standard in England and many other countries. I recently tuned my Weihrauch HW100 to 11 fpe, and the shot count and noise are both greatly enhanced.
 
Lets say your shooting H&N pellets, in most cases pistol shooters would favor the "light" 7.56gr pellets and rifle shooters would use the regular 8.18gr pellets

- For what it's worth, at my level of shooting (older guy who like to punch whole in paper). I use the standard 8.18gr pellets for both 10M rifle and pistol

  • The H&N Sport has served me well as a "practice" pellet, and shooting pistol, I cannot honestly say that I've noticed much of a difference in group/score VS the Match pellets. For 10M rifle, it seems to have more flyers than the Match... but than again, maybe I'm just concentrating more when shooting the more expensive stuff ;-)
  • Many (not to say most) recent ISSF air gun will have a F-in-pentagon stamp on the side, to show they comply with the German 7.5J air gun regulation (as in, it's considered a airgun and not a firearm). That's about 560fps with a 8gr pellet. 
  • Canadian shooters will have their gun set to shoot at under 500fps (again, to conform to some contorted regulation)
 
In my years of 10 meter shooting most all rifles are anywhere from 480 to about 600 fps and shoot the popular 8.3 gn wadcutter pellets. Yes some find a slightly lighter or heavier wadcutter pellet. In actual competition there are strict regulations and they may have changed over the years since my competition days. My own 75TO1 match rifle is most accurate with 8.3 gn wadcutter pellets at 565 fps velocity. 
 
As you get more $eriou$ly into the game, match pellets are also available in various diameter, to better suit whatever your air pistol/rifle might prefer.

From https://www.tenrings.co.uk/pellet-testing/  Steyr LG10E. Ten shots were fired using the RWS R10 4.49 

505 fps 504fps 501fps 500fps 502fps

499fps 503fps 501fps 499fps 504fps

The average velocity was 501fps with a deviation of 6fps.