If you want tactical acumen, don't read the fluff... that's more about mad faith and insane 'heroism' (wrt Space Marines, at least).
The key to WH40K is gauging distance more than anything else. Tactically, it's all very set-piece, none of which is particularly applicable for modern warfare. It translates to the operational level tentatively at best, though there are only really two broad tactics that are used (based on both sides acting aggressively): reverse-Cannae style horns-of-the-bull; and echelon/refused flank. So it is often the case that the result of a battle can be decided (on a 6' by 4' at least) by deployment alone. Adopting a short battle line between two major pieces of terrain and bulking up one flank is what wins me my fights (though it depends on which list I'm fielding).
Tactical reserves and genuine manouevring don't play much part since the charge and shooting is mainly distance based, and countercharging doesn't really happen. In a sense, you're better off getting one of the newer TW titles and playing battles on the uber-hard option with camera restriction.
Still, if you want a list that will really stretch your abilities as a commander, go for either Eldar or Dark Eldar. Eldar because all of their units are good or awesome at one thing and complete and utter shite at everything else, so you've got to delegate their roles on the battlefield very carefully. And as for Dark Eldar, they are fast, they are hard-hitting, but damn they die easily. With them, there's a tenet that veteran gamers use 'two-round-kill' (i.e. two rounds of CC to kill an enemy unit so they charge into CC your turn, and freed to continue in your next turn). They have to be used intelligently or you'll lose by turn three.
If you get good with those two army lists, you'll understand how to use particular qualities of troops you command, corny as that sounds, but the implicit knowledge/experience is worth it.
However, having said that, they do not make good starter armies since they die easily. If you want something akin to what you're going to do, then I'm with Pandalisk, Imperial Guard. They die easily too, but their weapon loadout (and tanks, learn to love the tanks) is probably the most appropriate.