The ability to print directly from the camera to the printer is called PictBridge. Most cameras and printers currently do have that function build in to them. HP is good, but recently, I've been getting frustrated with the life of the newer cartridges that they put into some of their newer machines. Another good alternative is Epson, they have quite possibly the BEST print quality for pictures, and the ink resists fading longer than the HP ink. Plus, the Epson ink dries practically instantaniously upon hitting the paper, so that you can touch the print a lot sooner. HP will take awhile to dry, especially if it is a print that has a decent amount of black in it.
The main thing to consider is if your mother will be directly from the camera or printer most of the time, or using the computer. If she is looking to print from the camera or printer (a little harder, but not impossible) then you should get her something with a color preview screen so she can see what it looks like before printing it. Otherwise, if she is looking to print from the computer, then the preview screen does not matter. If you are looking for some specific recommendations of printers then here are some of the best ones for less than $250. All of these would be fine:
1. Epson R320(screen) - about $180
2. HP Photosmart 8150(screen) - about $180
3. HP Photosmart 8450(screen) - about $230
4. Epson R200(no screen) - about $100
One other thing to note is the cartridges that the printer will be using...
Epson:
Epsons use individual color cartridges that allow you to fully use the ink before having to replace it. Furthermore, the Epson cartrides also usually have a longer life than the HP.
HP:
HP uses a tri-color ink system that sometimes can lead to some unused ink being thrown away, therefore not lending as much to cost efficiency. When looking for an HP printer, try to buy one with the 96/97 cartridges in it. The printers usually cost a little more, but you will make up that cost in the ink in a VERY short amount of time (the 96/97 have almost twice the amount of ink in the cartridges).
Page yield information on the cartridges can be found out at the respective web sites of both companies. Let me know if you have any more questions, I will be more than willing to offer any more advice

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