Welcome aboard.
First, you should know that the 357Max will have to be built or bought USED. IMO, I would decide between the 223 and the 308 and go get one. Then, send it off for the other barrel. As far as the 357 Max goes, I don't beleive the factory has any of those left, but last I checked a couple weeks ago, they still had some 357 Mag barrels. You could always have one of those fitted at the same time and then have it reamed to a Max.
That's the way I would do it.
Good Luck, Cookieman.