It sounds like you're looking to get into long range shooting for real.
With that plan I would strongly recommend getting Mil based scopes. Its not just a Tacticool fad, it's like cheating when making shot adjustments at long range.
You can do the same thing with MOA based scopes like Vortex because their reticles and dials are matched, ie MOA reticle/ MOA dials. But when shooting long range you typically have someone else with you for spotting, etc. and most people I shoot around have all gone to Mil based scopes and spotting scopes which makes math virtually nonexistent except ranging unknown distance targets. It's just my opinion, but I think you'll find the find the platfrom much more user friendly once you've used it.
The only person I shoot long range with still running an MOA scope is a Vortex Razor HD gen 1 that he only chose MOA because he has a Gunwerks range finder that is in MOA only ( why they haven't done a Mil version is beyond me).
There are good deals out there on gen 1 razors with Mil reticles.
Back to your question concerning 338 LM, the PST should do it well if cost is an issue. At those long ranges, on a big bore gun, you want great glass, bullet-proof build, magnification, large internal adjustment range, and fine reticle subtensions. Targets at 2000m get really small behind thick reticles. Some Vortex reticles get kind of thick. Look for the thin ones. All of those requirements are why the cost of long range effective scopes get high fast.