Billy, besides your military background, you do not give us any info on your marksmanship background nor info on any other rifles you possess.
For learning technique, shooting a 338 Lapua is a waste and probably counter productive. You are more likely to run out of money and gumption before "arriving". Even the US Marine sniper corps do not approach the subject this way.
A far better way to start is with a low recoil rifle, setup properly to shoot high BC bullets. Something like a 6.5x47 or a 6.5x55, either with an 8 twist match barrel. There are many good quality 140gr low drag bullets (Sierra, Berger, Lapua etc). If you don't have something like that, you can get set up for probably under $900 by buying a used Savage base rifle (model 10 tactical or 12 VLP) and then fitting a Shilen prefit barrel yourself, doing a good bedding job and fitting a good 1 piece 20MOA scope base.
If you have a 243 Win already, that could be re-barreled with a 1:8 twist barrel and you could shoot 105gr SMK bullets or Berger VLD's or thre 105gr Amax. You could even go with a Savage model 10 in 223 and fit a 1:8 twist Wylde chambered barrel and shoot 80gr Berger VLD's. People shoot those out to 1000 yards.
The point is, you want something that is inherently accurate, low recoil, shooting the best bullets for the caliber that exist. Then the outcome on the day is dependent on you. That is very important. The 6.5 calibers listed above are not barrel burners, nor is a 223, nor is a 308. The 243 will likely have the shortest barrel life. I did not list a 308 as a primary trainer since it has sufficient recoil with a 175+ grain bullet to make it a step up the skill chain to shoot accurately on a regular basis.
The objective is to shoot at 100-whatever range is available on a regular basis, practising technique (range, wind, dope, dial, shoot, record results). Just blasting away until one connects a steel plate is not going to help you make a good first shot the next time.
Once you reach a point where you are consistently making excellent shots with the "trainer" rifle, now is the time to get out the bigger iron. When range day comes, first shoot the trainer rifle. If you are on form, then see what you can do with the big rifle. Don't do too much at 1 time. It is easy to develop a flinch or become frustrated since all higher recoiling rifles are going to tend to be less forgiving on the manner and consistency of the way that they are held. They are harder on the bedding too and most of the time with factory rifles there will be bugs that you have to iron out with the stock and bedding and action screw torque.
If you seem to be screwing it up, put down the big gun and pick up the small one and see if you have learned any new bad habits. If you cant shoot the small gun consistently, you need to work out your issues till you are back on form again and deal with any problems the bigger rifle may have. Try using a benchrest type front support with a bag instead of a bipod since some people may battle to shoot well off a bipod. Once you shoot well and develop confidence, you can "expand the envelope" by trying the bipod again.
I have a model 10PC in 223 and used to only shoot Hornady 75gr HPBT bullets (due to factory twist rate limitation) and I have had several non shooters shoot that rifle for the first time at 160 and 320 yards and every one of them shot better than 2moa at 320 yards on their first attempt. Of course I applied elevation and drop correction for them and set parallax. In the meantime I have a 26" 1:8 barrel on it and am developing 80gr Berger loads for it. That rifle will always let me know if I am on my game and it is very inexpensive to shoot. My 243 is a 1/2 MOA rifle with 95gr Bergers and is my primary coyote hunting rifle. But since its barrel will not last forever, I am pretty sparing in its use.
I have a 308 that was built on a model 10 receiver which will shoot 0.25" groups if I am in the right frame of mind and body. I am shooting 175gr SMK bullets out of that. It is my "step 2" rifle. Ballistically not the match of the 243 since it is slower, thus wind correction needs to be precise. With significantly greater recoil, it is harder to shoot a similar size group as the 223 and I could not keep doing it for the same length of time. But still relatively cheap to shoot and will last a long time. Then I have a 6.5x284 which is very capable for something below magnum status. Very good ballistics with the 140gr Hybrid VLD's, lots of speed. Fairly comparable to the 308 in recoil. Of course the barrel will have the shortest life out of all my rifles and initial load development can sometimes use up 1/4 or half of the potential barrel life. If you have not thought about it before, equipment life is simply something to consider. Any magnum and a lot of non magnums do not have infinite barrel life and will not last forever if shot regularly. The more accurate the barrel, sadly, the sooner you will notice any degradation. That is why people think AR-15 barrels last forever when they start out shooting 2.5moa... With every new barrel, you will be adapting your reloads and you may have to adjust them during the life of the barrel to take throat wear into account. If one only shoots 50 rounds every few months then of course the barrel may last you for the rest of your life.
Best of luck and clearly, my advice is to start small, work up. When in doubt, go back to the small gun and check that you are doing everything right....
