Firearms are probably one of your best bets for surviving the initial infection event and immediately afterwards. At least in the US. I know of about a dozen places within ten miles of me where I could stock up on ammo and firearms with my crowbar credit card.
The S&W .50 caliber or Israeli made Desert Eagle would make a mess of anyone's skull not just zombies. Additionally with smaller caliber weapons, especially automatics hits to the legs would eventually impede their motion as joints don't like to work when pummeled repeatedly with lead at high velocity.
Shotguns are your best friend but here I'd go with the old movie cliche of starting with a fully loaded police or military style and when empty simply drop and move on to something else. Reloading is something that should be done after the action is over. (Yes I'm aware of the irony of using a cliche)
The luxury of downtime is not one that should be counted on. Or having more weapons with bullets than zombies, especially in urban areas. Which is why a hand-to-hand weapon is probably your most reliable companion, though a gun does make sense at a distance. The Desert Eagle is a fine, powerful weapon that you need two hands, a stock, and a firm stance to have a hope of controlling the recoil and making a few dozen quick shots. And after a bit of firing it your arms
hurt (oh, my misspent Rifle Team days [note: we shot .22 rifles at small black dots, the Desert Eagle bit was with a Teammate's parent after, and it happened in a range. It also helped take down my masculine bravado a few rungs, which in retrospect was not a bad thing.]). I'd stick with something smaller, and with ammo that's easier to find. Something like the old M1 Carbine, that you can use fairly accurately and move around easily.
Additionally, and this is something that scared the heck out of me when I learned it, grenades are legal here in AZ. They're expensive as hell and require A LOT of red tape and paperwork to acquire but if you have money and the time they're yours. What this means is that I know of two different stores in Phoenix that stock and sell them.
Which only really slows down, unless you get lucky and some shrapnel takes care of the brain. There's no guarantee that the force of the impact will really do much to a zombie, apart from knocking them back/delegging them.
Which brings me to my next point, automatic weapons. Easily gotten in some states even the lighter caliber ones will deter zombies by shear transferal of a lot of kinetic energy. The 45 calibers ones would chew some serious Zombie mobs to pieces.
Yeah, but they you just end up with a zombie mob that's crawling, or moving a little faster because it's lost some weight. The lack of an arm or most of a midsection might slow the zombie down, but it doesn't kill them. In the worst case, you end up with a bunch of crawling zombies that you don't necessarily see as well as the upright ones.
Plus the transferal of momentum will only really happen that efficiently if the bullet hits bone, which isn't guaranteed. It's not the movies, where a bullet sends a guy flying feet back into a window. A regular bullet isn't that highly kinetic (High speed but low mass), and won't transfer that much of anything while passing through soft tissue, even if it's designed to break up.
