Hi there and again, welcome to THR. I'm going to go over some costs involved in the wonderful world of shooting, since that was one of your concerns (unknown financial obligations).
If anyone feels I'm wrong with any of this, feel free to chime in.
First, by all accounts, the Sig P250 should be a fine pistol and, if cared for, would probably not need much maintenance aside from cleaning. This is also probably true for a used pistol (depending on who took care of it previously), though buying new means you know the gun's history, because you've taken care of it.
Any questions about the purchase can definitely be asked at a gun shop - they're going to know what fees and such might be involved in the purchase in your state (wish I lived in TX!) better than me.
Okay, so let's say that you buy the gun online. The purchase price may or may not include shipping (budsgunshop.com includes shipping in their price). The website ships the gun to a local firearms dealer, where you're going to pick it up. You pay the website who you bought the gun from for the gun/shipping, AND you then pay the firearms dealer where you pick the gun up, for a "transfer fee." I think that usually also covers the federal background check as well. Call any shop and ask - the fees can vary from shop to shop, so get one convenient for you and at a fair price.
Ammo, as you've said, can be expensive. 9mm isn't too bad. Price varies by caliber and quality of ammo. Buy more ammo than you think you'd need - you'll likely go through it fast. Get used to handling your gun safely, cleaning it, and shooting it.
You'll also need some gun cleaning supplies. You can usually buy a little kit that contains all that you need. Sometimes the kits are specific to a certain caliber - others have a variety of calibers. The kit should contain brushes, some "patches", bore cleaner, gun oil, and a cleaning rod. The rod is used to push the brushes and patches through the gun's barrel, to get rid of lead remnants, powder, etc. These kits are relatively cheap, around $15-$20 for a single caliber...more expensive for multi-caliber kits.
Clean your gun when you get it! It'll help you familiarize yourself with it, and it ensures the gun is in proper condition to shoot. Read the manual if it came with one. No really, read it
Go online and look for one if you didn't get one when you bought the gun.
Now that you've got the gun, and you can clean it (clean it regularly, take care of your firearms and they should function longer without issues), you're going to need to keep it somewhere.
A little gun safe/vault is an option (the kind that can slide under a bed), or more than likely a new gun will include some kind of lock of some sort. I recommend using the lock - if not for any children you might have, so that if you happen upon a bad guy mid-heist in your place, you don't find him pointing your own gun at you using your awesome self-defense rounds. Also, safely storing your gun away is just a good practice. If your gun will be used for self defense/carry, then obviously locking it up all of the time wouldn't make as much sense. Some people apparently like
these little safes for $40 or so. I'm considering getting one of those and latching the case to my bed frame.
Bottom line: Your transfer fee shouldn't be more than around $50. It depends on your area. Gun cleaning kit/supplies - $20+, if you can find a cheaper kit it'll do what you need, otherwise ask for cleaning supplies when you buy the gun. Ammo - varies in price. Gun lock/vault - gun might come with a lock, but that case above is only $40, vaults can be around $100 or you could invest in a gun safe....necessitating more gun purchases to fill the safe!
Hope some of that helps you a bit. Good luck with your first firearm purchase! Get what you like, and enjoy it! Be safe and have fun!