If you want target shooting in a Short action and want mid range and potentially long range then the 6.5 Creedmoor would be a perfect fit if you want something easy to shoot and widely available, especially since you already have that caliber.
The 6mm versions such as the 6mm Creedmoor are great if you want tight groups at closer ranges, but if you plan to push to the 1000yrd range, the 6.5 range would be a good way to go.
There are also things like the Lapua 6.5x47 that are quite popular.
A lot depends on do you plan to reload all your ammo mostly, or do you want a cartridge that you can grab great off the shelf ammo?
Now if you are planning on trying to be tops in the benchrest world and will hand load all your ammo, then there is a whole world of barrel burning wildcat rounds that get amazing results and require a stack of spare barrels.