I'll throw my vote in for an older, used Singer as well.
They are built like tanks and are really hard to break. One from the 50's or 60's would be something that could be found at a repair store or even a garage sale. Throw in a 50 dollar tune up and it would still work out cheaper than buying a new machine.
You can sometimes find the really old singers at garage sales masquerading as end tables (the machine folds down into the table)...

Mine is a hundred year old treadle (foot powered, non electric) and it sews everything including layers of leather and very thick fabric (I recently discovered that it will also sew through my finger...sigh). It only has one stitch but I've made clothes, toys, bags, pads, diapers and assorted other stuff with relative ease.
The only issue I've had with it is that the tension can get screwy on very thin fabric (they didn't have polyester 100 years ago, fancy that). Oh! and that my kids like to pump the treadle like it is an exercise machine and have stretched out the leather band that turns the wheel on it. Fortunately we live in Mennonite country and these old machines are everywhere and we have a singer store in town that sells the leather bands and all the parts I could ever need.
If you do decide on a newer machine I don't have any particular recommendations but I would suggest getting one with less stitch options and no computerized aspects as that way there is less to break down and less fiddling.
Good luck and happy hunting!

I had a cheap brother in the states, and it got the jobs done. I could tell it wasn't an amazing machine, but i never ended up cursing its name or maker. And i made lots and lots of pads and projects with that puppy. Now I've got this little Italian baby that the shop keeper told me that most of the internal parts are manufactured by the same company that manufactures parts for Bernina. So i suppose that's a reccommendation for bernina.
Anyway, free cycle and craig's list are the bomb and everything, but if your mom isn't hip to that stuff (i know my mom wouldn't get me anything there- it would weird her out)... I don't see a real problem with getting a brother to putz around with for a while until you find out if its something you're really going to develop a passion for and want to upgrade on- or if it's something that's gonna spend lots of quality time in the closet because you are one busy woman.

I agree with the older machines, and specifically with madame filth... a singer from the 60s if you can find one.
I had a 1961 Singer Slant-o-Matic and she was aMAZing...
could sew through everything, had a million stitches, and a button holer attachment.
Heavy duty and great. And yes, find someone who can work with old machines.
...unfortunately i lost my singer in the house fire a couple of years ago and haven't found anything as good since.
Good luck and Have Fun with the shopping around!

Basically what everyone else already said. I just went through the whole researching for a new machine a couple of months ago, and this what I gathered from all of my searching:
-New Singers are all crap.
-Any machine under like $300-$400= sketchy quality.
-Check your local vacuum and sewing machine repair shop.
-Everyone gushes about old machines, but just be careful. Make sure your local shop is knowledgeable on that brand and can repair it if it breaks.

I got a vintage machine and she was so purty and ran decent once I got her tuned up, but she could not hold up to the jobs I needed her for. Basically it really depends on what you're going to use it for. If it's for occasional fun use and nothing more then it really doesn't matter too much. But if you plan on using it a lot or having it for a long time and growing into it, then it needs to be solid. The problem with new machines is that the internal parts are made of plastic and break easily. That's why old machines are such workhorses, they are all metal and just last forever. I ended up getting an Elna 2600, which is part of the Janome family. I got her (yes, all sewing machines are her to me) new at my local repair shop. She was on sale and I got a $50 trade in value on my old machine, so I paid about $200 for her, regular retail was closer to $300. Her outer case is plastic to cut down on the weight, but all of the internal parts are metal. It's been a great machine so far, runs smooth and gives me nice stitches each time. My mom has a Janome that she paid about $400 for a few years ago and that is a great machine, too. I love using her machine, so quiet and steady.
Just check out Craigslist religiously, you never know what you'll find posted there. I see a lot of machines listed that are really decent newer machines for beginners for really cheap. A lot of Brothers, which I've heard pretty consistent good things about. And thrift shops, or even Ebay. There are a ton of vintage machines on Ebay. Good luck!

the best are probably Bernina and Janome. I agree, a cheap machine is usually not worth the trouble. Used ones are a good idea, my mom's old Singer is much better than a newer one I once had. The only problem with used ones is finding replacement parts. Tell your mom to try yard sales and craig's list. And read the book that goes with it or check out a book from the library. Totally necessary. I've been sewing since I was 12 and I have owned many sewing machines of different brands (I move a lot and give them to friends when I go) and though the concept is the same, there are usually little differences that will drive you insane if you aren't aware of them. That said, my current machine is a piece of plastic crap but I get the basics done on it. I will be saving my yen for a Bernina and a serger after my next move to a giant city with a five storey fabric store near my new job. five. storey. crazy.
anyway, good luck and happy sewing!

a singer from the 60's. i recommend getting an old one. in my research i found that the good new machines are like a thousand dollars. anything cheaper than that, even the singers, are plastic crap. i recommend you go to a sew-vac store, a place that takes trade ins, refurbishes and resells.

there is one brand, a european brand, that's the exception to the new rule. i'll have to rack my brain to remember it.

I got a brother brand one from Target a few years ago, nothing fancy but not bottom of the line either. It was eh. I mean once I semi figured out what I was doing (and I'm still no expert) it was not that great. Everyone who knew told me I just needed an old solid machine. Someone offered a 20 year old Sears model on freecycle that weighs about 10lbs more than the one from Target and it's great. I did take it for a little tune-up at the sewing machine repair shop and it's just perfect for me now.

So that doesn't help as far as what to buy for new! But maybe you could get one off of freecycle now and have your mom spring for some classes or the sewing machine tune up for you?