Wildcatting is a ton of fun and really a lost art these days... There are plenty of factory chamberings that leave very little to want BUT there might just be an itch that needs to be scratched... and making it your way might just be the way to solve that.
For target shooting, you need to look back in time to the Post WWII era to the 70's. here you will find the vast majority of what we today call, NEW cartridges. Yep, it has all pretty much been done long before the internet was even a concept. Hell, phones were still attached to walls with a "friendly" operator connecting your calls.
Parent brass was not easy to find so shooter mucked about with what they had and came up with some real gems. Also, alot of brave and curious engineers making all sorts of weird stuff including SMALL Primer 308 cases which eventually spawned the BR family. No, the 6BR NORMA is not a Scandinavian idea... nor is the 338 Lapua.
From the 22-250 (also a wildcat in its day), you can build the X47 Lapuas, Creedmoors, XC's. you can thank Handgun Silhouette for many of these mid sizes cases... google Elgan Gates and IHMSA.
From the 7.62X39, you can build the PPCs, Grendels
From the 223, you can build 222, 6X222, 6X223, all the TCU family (you want fun, have a look at these), Fireballs, Black out/Whisper (yep, the AACblack out is a copy).
From the 308, everything from 22 to 358.. not sure if they ever got to 40cal (more then likely they did?)
From the 30-06, from the 6-06 to the 401 something or other
From the 30-30/225 Win, TONS of wildcats and companies that exist playing with rimmed cartridges and single shot firearms.
From the Mauser, 6mm Rem to kind of Swede (at least the 6.5X57 which IS a cartridge) to large metric bores
From the 300H&H, you can get to all the belted magnums including many Wby's
From the 404 Jeffery and 416 Rigby, pretty much everything else in the boomer world including the Lapua, Lazzeroni, RUMs, Dakotas, etc.
There are literally hundreds more that I have not listed that have been modded from rimmed, rimless, rebatted and belted cases.
Get the book Cartridges of the World for a really cool look through time at the thousands of cartridges that have been created... and this book is no where near complete.
Enjoy... lots of fun and if you want to perfect your knowledge for reloading, Wildcatting is how to you do it.
Jerry