What kind of optics do you have? There are plenty of off the shelf rifles that will shoot 1 MOA or better now days. The trick to the whole thing is the optics. You WILL NOT get any long range shooting accomplished without the right optics.
So start with the best optics out there... the ole MKI Eyeball!
Best thing I ever did to start shooting long distance was learn on iron sights. That got me into M1 Garands and shooting those accurately out to 500y! Something very satisfying about hearing the gongs ring at those distances using iron sights. After that experience, using scoped rifles actually felt like cheating! The same guys that taught me competed in the Woodys DMM with a old iron sight, bolt action Enfield and made a dam fine showing out of it!! The 600y targets were a bit of an issue for him, but he scored WAY higher than me over all and I had a scoped 700! He knows his rifle and how to use it effectively.. and he practices regularly!!
Everyone's advise to learn your current rifles first before wasting time and money is spot on! You said you had no youth matches near you?? What have you tried?? There are many youth oriented org's... you just have to look a little! Try these...
Appleseed - appleseedinfo.org - Great group of people supporting history and marksmanship. Teach you great skill sets that will translate into lifetime shooting skills, and you get to learn a lot you'll never get to hear while in school. Heck, a weekend here and my 13yo was impressing his history teachers!! Grab a .22LR and go visit them.. they have events in MO!
CMP - odcmp.org - Their club and competition tracker showed about a dozen comps in your state. If you like long range stuff too, they sell great M1 Garands (bought 3 so far!) cheap and then your in the high power shooting realms. Camp Perry is just a little drive from you!
4H Club - The 4H Clubs usually are connected to the local High Schools for shooting since the schools can't handle the liability. Find your local 4H Office and ask them to point you in the right direction. There were 14 different shooting programs in the local school system I found after looking them up!
Any tactical shooting comp - My son and I just found these in our area and we are in love. We've attended one, watched another and continue to learn about ways to improve. We also found a local .22LR tactical comp that gives you all the learning and skills, but at a fraction of the price! You want to hone your wind and drop skills, shoot a .22LR out to 300y and still hit 1 MOA or less!
I can tell you from direct experience... you cannot buy skill. I thought I could and I was wrong. You must learn it and the more you challenge yourself in the beginning, the easier it is to evolve later on. I have a nice R700 .308 with a scope and all the whistles, but I still love shooting the M1 because it proves I know what I am doing when I pull the trigger and hit that 500y target. My son also likes using iron sights.. asks me regularly to pull out the rifles with it on them to play with! It makes me proud that he embraces them and likes to use them as much as his Savage 12 LRP.
Learn the skills and save your pennies for tools that will serve you better in the long run. How do you hit those 1000y targets? Same way you get to Carnegie Hall... Practice, Practice... Practice. Anyone can buy a Stradivarius Violin... but you still have to learn how to play it properly!
Good Luck in what ever path you choose!
KS
P.S. I'd start with the .308 simply because the resources and variety are there no matter where you go. If your starting out, the 6.5C might be a bit of a handicap, since your local resources might be a bit sparse. Find a local group and let them guide you until you gain the wisdom to make these bigger choices on your informed self decisions!