I don't know if he hand loads or not but either way I like the 308 above all for learning. It has low recoil and great factory match 168 and 175 in Federal and Black Hills. The 7-08 and 260 are great cartridges BUT for learning I like the 308. It is not as forgiving as a 260 with 140's or a 7-08 with a 162+ and thats why I like it, it will force you to learn to shoot conditions and when you move on you will be a better shooter for it. Long range is a constant learning sport that can humble you at any time blush
I like both the 300win and 7rem and both are performers with the right bullet. 7mm 162's through the new 180 Berger Hybrid and 30 cal 215 and 230 Hybrids all bring a new level of performance.
I have found over the years with the more I've learned and became comfortable with long range I often use less gun / non magnums for long range deer. Of course this depends on conditions and set up. When you mention Elk, I have my own feelings not to start a poop storm and I know fist hand some small cartridges can kill a long way out, But there are times and conditions that will cause me to grab the 338 and hit them hard with a 300 grainer and not apologize for it laugh