Thanks for the fast response.
My only concern with such a microphone is that the person the gift is intended for is a strong singer and that the sound would distort at higher volumes. I'd prefer to spend more money if it means the quality of the recording will increase significantly.
Well see, you're still leaving it a bit too open.
How much are you willing to spend?
With every increase, you can see a big jump in recording quality.
A used SM58 and a cheapish USB interface will run you in the range you initially quoted.
Double it, and you could probably noticeably improve your quality.
Double it again, and once again you could get a noticeable improvement.
You could spend upwards of $5000 for a single microphone and interface.
And the quality of the recording would increase significantly.
If professional results are desired, there's going to be a whole lot more going into it than simply buying the right mic.
Room treatment along with some solid know-how about mic placement and mic technique are gonna play into it. It doesn't matter how nice the mic is - if it records the sound of her voice reverberating around an ugly sounding room (or even too much of it reverberating around a nice sounding room), you'll never get it to merge naturally with the backing track.
There's also the know-how that it will take to get the vocal to merge with the backing track.
Even a professionally recorded vocal part can be very hard to sit into a mix that has already been mixed and mastered. One generally mixes with all the instruments - voice included - in mind, and so you might end up finding that there are some backing tracks that just won't ever have room for the vocal to sit naturally.
If you aren't looking for professional results, I'd say start small and work with what you have.
That USB mic might be the ticket, and the fact that it might distort on louder passages may actually be an advantage, as having to work around that could be a great way for your singer to start to learn proper mic technique.
If every time she makes an "s" sound the mic picks up a very harsh amount of sibilance, she'll have to start learning to pull those sounds back a bit. If every "P" creates a pop, she'll have to learn how to still convey the p sound without that big explosion of air. If loud passages make the mic distort, she'll have to learn to lean back a bit to make sure that when she goes loud the sound remains consistent.
These sorts of techniques are crucial in singing well with a microphone, and once a singer internalizes them to the point where they're automatic, it helps make all her vocal work with any microphone sound that much more natural.
There are downsides to the USB mic, though.
Many of them don't have monitoring capabilities built in, so it takes a good bit of effort to make it so you can hear what you're singing while you sing it. Also, the sound quality on many of them is believed by many to be pretty low for music recording.
If you decide to go the route of an interface combined with a microphone, you might look into something that allows live monitoring of the input signal.
The Lexicon Alpha may be the sort of thing you need.
It has a headphone amplifier in it and a "mix control" knob on the front which allows you to dial into the headphone mix the ratio between the already-recorded backing track and the live track that is being recorded. Fairly convenient and simple to operate, and it comes with recording software included.
As far as the microphone goes, you might look at a couple of different threads on this site, starting with these:
https://homerecording.com/bbs/showthread.php?t=311197
and
https://homerecording.com/bbs/showthread.php?t=302579
Either way, as I said, you could easily spend thousands of dollars and still not get pro quality, so if that's your goal, I'd make a gift of some studio time rather than a microphone, but if you're simply looking for something to help her improve her singing and hear an approximation of how she might sound over those backing tracks, I'd keep it simple and cheap and remember that most of the improvements in one's recorded sound can't be bought - they have to be earned through hard work and experience.
Good luck.
