Of those loads on that page, I'd say try the 90-grain XTP. I've had very good luck with xtp bullets accuracy-wise.
That said, it's not the cheapest option at $13.99/25, but I wouldn't advise burning tons of rounds thru an LCP on a regular basis anyway. I carry an LCP daily. Sometimes by itself, often as a backup to a larger gun. It's a great little gun and I trust it implicitly, but I wouldn't expect its life-expectancy (in round count) to be up there with a PPK or other, heavier guns. It's bare minimum construction-wise, and its lifespan is likely to reflect that. Don't know how many rounds I've put thru it in the ~5 years I've had it, but it's almost certainly not 1,500 and may not be much over 1,000. Some other guns, I'll do that many rounds i a month or two; but in the LCP, I can't help but wonder what percentage of the gun's useful life that 1k or so rounds represents..?
Agree completely about wanting to be as competent as possible with it, but I also agree with two4spooky's point about the inherent limitations of this type of gun. Being a 9-oz DA-only gun with a sub-2" barrel, I expect the definition of 'proficient' to be pretty loose. To me; ymmv.
FWIW, the 90-grain XTP is one of the better .380 carry loads imo and is what I carry in my LCP. I'd suggest finding what load you plan to carry, and simply buy the same for your stash. If I were going to shoot a bunch of rounds thru my gun, it might as well be the load that I depend on on a regular basis. I like having what a lot of people consider "way too much" ammo on hand, but for this gun and a few others, I personally think that even a small stash of just several hundred is probably more than a lifetime supply for most people.