Re: .22LR trainer and .308 build
The first question you should probably ask yourself is WHAT DO <span style="text-decoration: underline">YOU</span> WANT?
There are generally two different schools of thought on rimfire trainers: 1) your rimfire trainer must almost identically mirror the "big bore" counterpart that is your primary rifle; or 2) your rimfire trainer is just a quality, reliable, accurate rifle that you can practice good position shooting, trigger control, ranging, dialing corrections for elevation/windage, etc., etc.
There are merits to both schools of thought, but what YOU want is what will be best for YOU.
In terms of your concerns about "starting all over" if you go traditional stock then you build your 308 using an AICS...I wouldn't worry about it that much as it should be a big problem. Yes, there are some muscle memory differences between the basic rifle stocks and the AICS and your hold/position on the rifle will be somewhat different, but more importantly, the fundamentals of accurate rifle shooting are the same.
Another thought...if you have not been behind an AI rifle or a rifle equipped with an AICS...get behind one and try it out before you drop the coin on a build (rimfire, centerfire or both). They are not for everyone and almost everyone I have met either loves or absolutely HATES the chassis...there isn't much in between. I happen to love the AI rifles and the AICS, but that is just my personal preference and observations.
Another important question to ask yourself is how much do you want to spend on your trainer before you drop the coin on a custom centerfire build? (Don't forget optics, mounts, etc.)? Going with an AICS-equipped trainer, you are basically stuck with a 40XB rimfire barreled action either stock or the action itself that you will have built out to your specs. This won't be cheap because by the time you find a 40XB rimfire (at $800+) and a Stage 2 Chassis (which you said you wanted...$950), you are pushing the $2k envelope without a single round fired in practice and without consideration of mounts/rings/optics/bipod/etc.
You don't necessarily need a multi-thousand dollar trainer topped with a $4000 S&B/Hensoldt/etc. scope, but you may want one. Your wants/needs and your budget really determines that first "leap" into the game.
With all that said, there is nothing wrong with less expensive trainer-type rifles, including CZ, Anschutz (little more $$), Savage, etc. You can get accuracy, reliability and a solid practice/trainer platform for a fraction of the money and you will still be achieving the most important thing...PRACTICE!!