The 9mm Parabellum is 9mm in diameter and 19mm in case length (not including the bullet), while the 10mm is 10mm x 25mm. They operate at similar pressures, so with the 10mm's extra ~62% volume it holds a lot more powder and is significantly stronger.
In addition to the great advice everyone has already given, I'd like to point out that over time the cost of ammo can easily dwarf the cost of the gun itself. Let's say you go shooting once a month to stay proficient with the gun (very important). And lets say you shoot 100 rounds each time, which is pretty reasonable for an hour at the range. I like to use Winchester 9mm 115gr FMJ (full metal jacket) ammo, which costs about $25 for a box of 100. It is not quite the cheapest, but definitely on the more affordable side. So that's $300 of ammunition per year. Shooting at the indoor ranges that are fairly common in the big cities/suburbs of Texas is around $10-15 per hour. So, let's take the low price and spend $120 per year at the range. Combined range and ammo fees for the year comes to $420, which is plenty to get a good gun. A few years of shooting and you've spent a lot more on ammo than guns. You're number may vary, but over a lifetime of shooting the cost of a gun becomes closer and closer to trivial compared to ammo, and any quality gun will last your life and longer.
I understand money being tight, so I was just trying to illustrate that ammo costs will trump gun costs over time, unless you like to buy a lot of guns and never shoot. I'd much rather buy few guns and shoot a lot.
There are also the costs of a concealed carry permit (both the state fees and cost of the class), holsters, cleaning equipment, additional training, etc.So, keeping that S&W to practice with .22lr is a good idea, especially if you get a revolver for protection. If you get a semi-auto, I would recommend getting a .22lr conversion kit if one exists, or a similar gun in .22lr. Aside from the financial aspects, practicing with .22lr is a great way to improve your shooting skills since the kick is so light. Also, the most important characteristic of any gun used for self protection is that you really like it. A gun that fits you well will be practiced with more frequently and used more effectively if needed, so get the gun that feels the best (which does not need to have any connection to price).
You'll find plenty of great info and some of the nicest folks around here.
