The choices of good firearms is rather large. As sugessted above, deciding on a trigger, action or platform style will narrow the field for you.
The SIG P220 is a great DA/SA platform for the 10MM Auto cartridge. I have had mine 6+ years now. I really like it as an overall firearm
My Colt Delta Gold Cup is exceptionally accurate. One of the most accurate autoloaders I own
I wish that Colt would revive the Gold Cup chambered for the 10MM Auto cartridge. This was discussed with Colt managment at this years SHOT Show. Unfortunately it is not in the cards at the moment. Colt did release a second variation of the Delta Government model at the 2017 SHOT Show, it has a equipment rail for those folks that like flashlights and lasers hanging off their firearm
The long discontinued Smith and Wesson 10xx family of auto loaders are both robust and soft shooting. However they have been climbing in price over the past few years. Parts and magazines are getting hard to find
EAA has some great pistols in their ELITE line. The Match Elite is a solid performer at a reasonable price. I am very fond of the Elite Pro.
There is also the Witness Hunter with it's 6" barrel and SA trigger it is a fine gun
Now the Smith and Wesson 310/610 family of revolvers opens up interesting territory
Since revolvers chambered for auto-loading cartridges head space on the moon clip and not the case mouth, this revolver can safely chamber and fire both the 10MM Auto cartridge and the 40 S&W. This gives you a very large selection of factory ammunition.
For those that hand load, the chambers on the 310/610 revolvers can be lengthened to accept the 10MM Magnum cartridge. This cartridge can give you an extra 200-400 FPS in velocity over the 10MM Auto cartridge
Then we come to custom built and converted firearms chambered for the 10MM Auto cartridge
Smith and Wesson's CS40 is built on the 45ACP frame and uses 10MM Auto magazines with a spacer in the back. It is a wonderful platform for a 24 ounce, 6+1 round, CS10 conversion
For something a bit larger and carrying one more round the Smith and Wesson 4013/4014/4053/4054 are also easy 10MM Auto conversions. Here is a 1014
The Mauser M2 is another great conversion gun. Due to the rotating barrel design this is the softest shooting pistol that I have ever fired that was chambered in 10MM Auto. It is a bit wide for some folks, but is holds 10+1 and is built like a tank
My favorite though is the 6" 1911 long slide that I built a few summers ago. The 6" barrel is a Briley mathc barrel with theur spherical bushing. The trigger rides on ball bearings for a very light, repeatable and safe trigger pull. The Aristocrat sight allows for 3 different ammunitions (or distances) to be set up all at once, very convienient fir hunting especially if you have a laser rangefinder on hand.
Obviously I am a Fan of the 10MM Auto cartridge. Hopefully you will become one also