Good first post! I was in the same boat just a few months ago, though I had become proficient shooting .22's (pistol & carbine).
Now, I voted 'neither' really cuz I'm just a stickler for details
I say go with the pistol/shotgun combo to satisfy your most immediate HD concerns. Nothing better in this world than a 12guage with the right lods for the job! That's partially because you cam get darn near ANY kind of load for it: birdshot & buckshot in any size you can imagine, slugs, flares, whatever. I can recommend a Mossberg 88 for HD or hunting (can get 'em for $150 at WalMart around here
w/ the long barrel, accessories and barrels are plentiful because they're identical to the 500 model in almost every respect; I dig it in 18.5" barrel for HD).
That said, go with a .45 for the pistol. You want to be sure you've got enough oomph if you're talkin HD. Springfield XD's go for $500 around here at Academy and hold 14 rounds! YEEHAW! So far the combo's running $650-$700.
Not bad for having $300 left to play with for ammo!
ALL THE ABOVE SAID WITH THE ASSUMPTION YOU'RE WILLING TO PUT IN THE PRACTICE TO BECOME PROFICIENT WITH YOUR NEW ARMS. Have fun!
Now, if you really want to see some fur fly, post your next one on "what's the best HD ammo for shotguns?"! (I say 3" T-shot; just trying to poke the hornets' nest!)