All this talk about putting a beginner a heavier recoiling rifle to prepare you for shooting a milder rifle baffles me. Obviously one can learn to control recoil on a .308 and shoot better with a 6.5. It there’s no reason you can’t learn the same fundamentals on a softer shooting gun. The fundamentals are the fundamentals. I learned to shoot with a Feinwerkbau pellet rifle in JROTC in high school and every lesson learned there transferred over to centerfire. Obviously learning to control recoil is a whole other animal but the one thing I know from pistol shooting is to never hand a beginner a heavy recoiling pistol first thinking they’ll be better with the softer shooting gun later. Put a beginner on a heavy recoiling rifle or pistol with no instruction and you have a potential for developing some bad habits.
However, Without more information from the OP , it’s impossible to say which gun is better for his situation.
If you are truly shooting inside of 500 yards and really just want to have fun, learn to shoot, and enjoy your time on the range then I would suggest a .223 bolt gun. Cheap to run, fun to shoot and in a brand like Tikka, plenty accurate with quality ammo. But .223 wasn’t on your list.
If you have more experience but haven’t had much instruction, and you plan to shoot longer distances, then the 6.5 is a perfect gun for the job. Easier to spot misses and correct for it. Plus it’s a fine long range caliber.
If you have plenty of experience with centerfire rifles and only plan to buy one gun for long range for the rest of your life and know the basics of managing recoil and FOM then by all means the .308 is a perfect caliber for the job.
Without more information though, you are just getting the opinions of guys based on their own experience. And they’re experience doesn’t necessarily apply to you and your goals.
I’ll offer my little bit of advice based on the title of your post. If you are truly a new shooter with no experience, and you don’t have a mentor or any kind of real instruction lined up, then of your two choices I’d recommend the 6.5. Yes you can learn all the nuance of how to better manage recoil with a heavier hitting rifle like the .308, But without an experienced shooter to help guide you, you might just find yourself getting beat up and not understanding why. Worse is the potential to develop a flinch or other bad habits that might be hard to get rid of down the road.
Just my two cents and that ain’t worth much. Have fun, be safe and welcome to the rabbit hole of high power rifles.
Hey I also learned my fundamentals with high quality air rifles, PCP "Field Target" air rifles in my case, in which the game requires astute wind reading skills and impeccable follow through. All of that, except recoil control, helped me to win long range championships with tactical rifles in Field Course style steel matches.
I just sold my 2nd to last 308, I'd sell the other one too but it's a family heirloom.
I trained my boys, my girl, and my wife how to shoot with airguns. They are all above average shooters. I have lots of stories about this subject I could share but the most recent one is this:
My 31 years old son got completely out of guns for the last 18 years. I got him shooting airguns then 22's when he was a young boy. By the time he was 13 years old I was the only person he struggled to beat in steel matches using his 9mm pistol. He just bought his first firearm a few months ago, a G19, man that guy can still shoot crazy good, it's like he never quit!!! The fundamentals were still there.
I can't stop, lol.
My 36 year old daughter has amazing natural talent with a gun, she's 4'11"/100lbs. Same thing, I started her off with pellet guns, then 22's. Exploits in the last few years - she was hitting a 5" rock at 700 yards with my 6x47L bolt rifle last year and hit all the steel present on the first shot, I was shaking my head because that was the first time she had shot long range??!! She's won almost every Field Target air rifle match she's shot in, beating a "world champion" female FT shooter, even winning a sponsorship??!! And during a trip to the range she absolutely humiliated the police training there next to us with my wifes friggen Glock 42 in 380??!! 3" group of 12 shots at 15Y in the 10 ring. They had trouble keeping all the shots on paper - ouch, I felt sorry for them. You should have seen the look on their faces!!!
And get this, she doesn't shoot guns unless she's visiting me??!!
Sorry, I just had to share.