I've been sewing for a long, long time and am fortunate enough to be able to work out of my home now on bridal fashions.
The first suggestion for a new seamstress (sewers are where the nasty water lives!) is to stay away from any machine that's advertised as perfect for new beginners. Sounds crazy, sure, but a good basic machine can last at least ten years and your daughter should be able to expand her skills over time without worrying about outgrowing the machine. Those "beginner" machines are inexpensive for a reason.
For a different reason, stay away from the most-expensive models, too. They're a marketer's dream, a seamstresses nightmare. They're priced as they are because of the multitude of features, most of which go unused by even the most experienced seamstresses. A fairly recent trend by the companies is to incorporate intricate embroidery features, but I don't recommend those machines either. The basic zigzag stitches should cover any embroidery embellishments; any more detailed work really requires a dedicated embroidery machine. Same thing with sewing machines that incorporate serger/overlock capability, it's simply too many features that don't work correctly; if she becomes proficient you can consider investing in a dedicated serger/overlock machine 3 or 4 years down the road.
You'll want these features: a straight stitch with easy shortening/lengthening, 4-7 different zigzag stitches with easy stitch-widening and -lengthening for both knit fabrics and embellishment, at least 2 buttonhole options for different weight fabrics, an automatic tension that can be manually adjusted, and several presser feet attachments for inserting different types of zippers and guiding different fabrics. I can't think of any machine line which doesn't offer all of these.
Singer used to be my favorite line when there were independent dealers, but not anymore. I found when I went looking to replace my machine last spring that the bodies of the new models are just too haphazardly put together and some of the parts that should be metal are now plastic. I searched around and ultimately bought a Husqvarna Viking model because of the machine's durability and the company's good name - the warranty and repair services are almost an extension of the machine itself. Also, you should consider the ease of acquiring accessories and replacement items (needles, presser feet, belts, etc.) - the machine is no good at all if it's sitting on the table with a broken needle and you don't know where to find one.
Ah, I'm writing a book, sorry. The last suggestion I have is, research your local fabric stores (not chains) and consider a gift certificate to one of them for your daughter. Then take her there after Christmas so that she can sit at the different models and get a feel for which one fits her best. The sales staff (if they're interested in educating a seamstress and not only the dollar) should provide invaluable advice and direct you and your daughter to a machine that will give her years of pleasure. Once you purchase the machine, the local shop will most likely offer classroom instruction - take them up on whatever they offer.
If you find that the only machines which will fit your budget are those you can find in Sears or Walmart, etc. at Christmas sale prices, I'd go with a Brother model before a Singer. If the choice is $200 or no machine, I'd take the machine and a good instruction book every time! It's a dying art and I love to see little girls become enthusiastic about it.