Gary's kinda right. What we think of as the "old west" was actually a relatively recent and limited period, probably somewhere around 1850 to 1890. Or thereabouts.
But, we're talking fantasy here, so I apologize.
Now, the "correct" answer is probably to bring a couple of John Browning designs, like a .45 and a machine gun, patent them, stroll over to the War Department, and be set for life. Be sure to write notes to your grandkids about buying GE and Microsoft stock, and suggest they not bet on the Cubs or Red Sox to win the pennant.
Personally, however, I'd head out to San Francisco and do some prospecting in the local rivers and creeks. Probably stop in the Black Hills along the way. That must have been an amazing rush for the folks who got there first. My son and I dabble in the prospecting thing, when we can get out west, and I can't imagine how cool it would be to be the first ones at what we now know were hot-spots.
Oh yeah, the point. For doing the prospecting thing, I'd bring the best AK-47 I could buy for the long gun, because of the reliability. Maybe a Bulgarian SLR-95 (??)--I'm not sure what's best, but I'd find out. With 700 rounds of ammo. For a handgun, God help me I'd probably bring a .45 Glock, again for reliability reasons, with the other 300 rounds. I'd be pretty vulnerable beyond about 250 yards, but those are my choices. Even in the wide-open west, most of the places you pan for gold don't have shots over 250-yards.