As odd as it sounds, I feel like I have a pretty good perspective as a relatively new sewer. My mother is a fairly accomplished sewer, but I was late to the game. I've now been doing it for a few years, and have come a long way, but remember very well my experience learning to sew and using a whole variety of different sewing machines. Hope this helps.
While generally with many things I cringe at the idea of newer, digital products (the affordable types) over older, quality items, in this instance the plastic nature of those machines may be more favorable for your teen. I have an older White sewing machine that was made when they were still a good company building in the U.S. Recently I had it serviced, and the guy who'd been working with sewing machines for 50 years told me to NEVER EVER EVER get rid of that machine, because, "They just don't make them like that anymore." Free arm, zero tension issues, front loader bobbin that is easy and gives me no problems, threading is crazy simple with a panel that opens to let me access the threading area, unlike some other machines. Only issue is a slightly more uneven feeding, but only by a hair from the other machines I've used. It's a beast, in a good way.
BUT...
It is heavy. And it's not even all metal like many of the much older ones. Only about 75%. When I first started sewing and had to help my sewing teacher with her ancient machine (she was elderly and couldn't manage), it was like lifting a load of bricks. My friend has an older Singer that I can struggle to lift from the ground to the table.
Unless you have a dedicated sewing area, it may be a bit much for your daughter (or you) to have to constantly set up and move an older machine. Or if she plans to carry it back and forth (to sewing classes, for example), it can be difficult.
Plus, those newer ones are simpler for new learners. As long as you don't mind possibly having to buy another, better machine down the road, it might be a good way to start out. Particularly as you don't know if it will catch on with her, and the easier machine might lessen the likelihood of enthusiasm-dampening frustration.
That being said, if you do get a used machine, get it serviced first. This is HUGE. You can't believe the difference on an older machine that has been serviced and one that hasn't. But expect to pay around $65-$75, and that's just for maintenance. Repairs cost more. And just so you know, this is actually something you should do every year if you can with any machine (depending on how often it's used). It should at least be oiled and cleaned regularly. Also, stock up on needles. If she starts sewing a lot, she'll learn eventually that using a new needles every few projects can make the difference between problems and problem-free sewing.
If you do opt for an older machines, check Goodwill. I don't see them a lot, but every now and again I see some awesome older Singers. I almost want to buy them just to display them
But again, take into consideration the cost of servicing/fixing them before you think you're getting a good deal.
You can also check pawn shops for newer and older machines. Not my first choice, but still an option.
Edited to add: a local sewing place I love had this webpage for sewing machine recommendations. It lists features they think are best as well as machines they like. Note: they don't sell machines, just classes and materials.
http://www.stitchlab.biz/sewing_machine_recs.html
