My post might not help you much, or at least you won't enjoy hearing it.
For defense ammo that you might need to defend yourself, your home or a loved one, leave "cheap" right out of the discussion. Any of the major ammo maker's performance defensive ammo is a fine choice but not of them can be termed inexpensive. Typically, you are looking at about a dollar per round.
On even a shoestring budget, you should buy 2 or 3 boxes of the stuff and practice with the first box or two, and carry or home-load the 3rd box. It's not like you have to replace the ammo often, it's good and will last for many years.
As for the S&W Sigma, it seems like a lot of gun for little money, but I would ask what your intentions are for it. If it's strictly for defensive use, that's one thing. If you are buying it to become a better shooter through extended practice and if you wish to buy it for fun range time, I would say to save your money. It literally has the worst trigger of just about any new handgun you can purchase.
Some folks have had luck in modifying the factory trigger, but that is best served for folks who know what they are doing. As a Sigma comes right out of the box, it's not much fun to shoot and it's not that easy to shoot well.
If nothing else, ask the salesman at the counter if he will allow you to dry fire it a couple of times before you agree to buy it.