I also would highly recommend Guns of the South. Not only is it a good novel, it is an interesting introduction to HT's strong points (good basic research, obvious knowledge and interest in subject matter, good understanding of time periods and historical characters) and weak points (use of many repetitive minor point of view characters and minor plot elements).
How Few Remain is also good, but not as effective as pure narrative fiction, especially for readers not clued into the premises of AH. I gave a copy to a co-worker who was a Civil War buff and he hated it.
HFR is also a prequel to the massive TL-191 series, which is overblown, poorly edited, and exhibits all of HT's faults and few of his virtues, especially in the later volumes. Nonetheless, the basic counterfactual TL is well-thought out, interesting, and plausible in the first (alt-WW1) sequence of books. The remaining (alt-WW2) books are highly predictable and unimaginative rehashes OTL-WW2 with the CSA standing in for the Nazis, although even there he does has some interesting touches which almost make the whole thing worthwhile. Almost. The whole TL from 1914 to 1946 could have been better presented in 3-4 books, rather than the 7 or 8 he used. When you can skip ahead 100 pages in a book and not miss any critical plot developments in the overall narrative something is wrong with his editor.
The World War megaseries is much, much more entertaining. Even though it has most of the same flaws as Tl-191, it doesn't take itself nearly as seriously. It's best enjoyed with a glass of Merlot and a sense of humor. Much more of a straight SF novel (Lizard aliens with sub-lightspeed spaceships, a military technology similar to ours today, and no experience in fighting wars for thousands of years invade Earth during WW2), it is both interesting and stupid at the same time. HT makes no effort to make the Aliens "alien" other than in their Lizard looks. In all other respects they are just incredibly dense people with no imagination or creativity. When they left home, we were just spear-wielding primitives. Too bad for them when they get here we have become much more technologically advanced - something they didn't expect. The Lizards get embroiled in a war with millions of Nazis, Soviets, Japanese, Brits, Yanks, and various other angry primates armed to the teeth and well-schooled in the arts of war. Even worse, they can't go home and they can't nuke us to death because they here to live. Just how many P-51s does it take to shoot down an F-22 Raptor, that is the question. You almost end up being on the Lizard's side as they are outnumbered, outthought, basically more decent than most humans.
You ought to be able to pick up story compliations including some HT stories at your local Borders/Barnes&Noble etc or a used book store.