Learning to sew is a lot like learning to drive. You don't need a fancy sports car to learn the skills. In fact, learning on an older, reliable car is sometimes better. But on the other hand, you do need a car on which the starter, motor, steering, and brakes work correctly and reliably. There's nothing more frustrating than trying to learn a new skill when the machinery doesn't work well.
So where does that leave the beginner sewing enthusiast?
You need a machine that will do an excellent straight stitch and zig zag stitch. Those two stitches will do almost everything you will need. It also needs to have a reverse. Just like a car, you sometimes need to drive forward and sometimes backwards.
I bought a car once without test driving it first. Big mistake. Now I insist on test driving the actual car I want to buy, not just another of the same make and model but the actual one I will be taking home. The same thing goes for sewing machines. Test drive before you buy.
The best value for a beginner sewing machine is a used machine. There are many times in life where we want something new, but this isn't one of them. A reliable sewing machine dealer that takes trade-ins will usually have an array of older machines that have all been serviced and are ready to go. These machines have years of use left in them and are a great investment.
You don't know yet whether sewing is something you are going to enjoy or whether it's just a passing fad. Investing 0 into a good, used sewing machine is much wiser than buying a new 9 inferior machine.
When you walk into the sewing machine store, browse the used machines and get a staff person to help you if you can. Tell him/her what you are looking for and what your budget is. Don't let him/her sell you something out of your price range.
Machines that are known to be "good" are ones with brand names like Singer, Elna, Janome, Husqvarna Viking, White, Brother, and Pfaff. I've had personal experience with White, Singer, Brother, and Elna. They will all feel a little different, just like cars.
Don't even consider the Walmart machine, the Kenmore (some are OK but you are taking your chances), or any other new, cheap machine. A good, spanking new sewing machine will cost 0-00 these days. If it's new and under 0, I wouldn't even look twice unless it's one of the brands I listed above.
You don't need a computerized machine or an embroidery machine but you do want an electric one. The antique treadle machines usually work great but you want to concentrate on learning to sew, not on working the treadle. Just make sure it has a regular household plug in.
Don't let claims like "1 Step Buttonholer" fool you. I've had a 1 step button hole maker on a couple of machines and, I actually prefer to make buttonholes "manually". These automatic buttonholers are not as great as they sound. If they get stuck or mess up, what a terrible job it is trying to rip out those stitches! All you really need to make a great button hole is a straight stitch, a zig zag stitch, forward and reverse, and a stitch length and width adjustment.
When test driving the machine, take some fabric with you. If you know you're going to be making jeans, take a 6" x 6" or so scrap of denim (even cut a piece from an old pair of jeans). The sewing machine store will have small pieces of light cotton fabric for you to test on. Those are fine but if you have a certain type of project in mind, make sure you take some representitive fabric.
Try the machine and see how it feels. Is the foot pedal sensitive enough? Is it too sensitive? Does it depress smoothly or is it jerky or sticky?
Can you smoothly sew a curve or is the machine foot sticky?
Does the machine sound like it is straining to run? Most of these machines are fairly noisy but you'll get a pretty good idea if the motor is running smoothly as you sew.
Check the bobbin out. (That's the tiny "spool" sitting below the needle.) Metal spools will last longer and are readily available. Price out the bobbins for the machine you are considering. Some bobbins are expensive or difficult to find. You will want to have lots of bobbins on hand.
Ask what kind of shank the machine has. You will need to know this if you buy any additional presser feet for the machine. There are 3 types: Low Shank (most popular), High Shank (adapters are available), or slant shank (least common). Low Shank presser feet are the easiest to find and often the least expensive. Write this shank type down if you buy the machine.
Also ask what feet are included with the machine. At the very least you will need a universal or zig zag foot and a zipper foot. If the machine does not come with both of these feet, buy them. An extra few dollars to have both of these machine feet is worth it.
Set the machine for a wide zig zag stitch and sew forward a few stitches then reverse over those stitches. Does the machine zig zag in reverse? Some will only sew straight in reverse. You don't want this.
Take the fabric scrap out of the machine after you have sewn on it quite a lot. Run your fingers over the stitches on top and bottom. Does it feel like they are raised above the fabric on one side? They should feel like they are laying very flat on the fabric without puckers. If anything feels amiss, the tension could need some tweaking. Have staff at the store do this for you. When you walk out with your machine, it should be sewing the very best it can.
Ask if the machine will handle a second spool of thread. Some machines have an extra spindle and some require an extra spindle to be added on. Some won't have any way to handle a second spool (you need to have an external spool holder for these). Having that extra spindle built in is a great time saver you will want. (It's used for twin needle stitching.)
Have the staff show you how to thread the machine and the bobbin and where the machine needs oil (if it does). Ask if they have the original manual for this machine. They seldom will but you can get most manuals online.
Ask how the upper and lower tensions are adjusted, how you wind bobbins, and how to adjust the pressure for the presser foot. Ask how to raise and lower the feed dogs and the presser foot. Ask how to change the stitch width and length and where the stitch selector and reverse are. Ask if the machine has a thread cutter (even if you don't use this, you want to know where it is so you don't cut yourself).
Before you are done, ask what accessories originally came with this machine and what the store has included with it. If lots of pieces are missing, the store may throw some replacements in for you. Ask if it has a carrying box or a dust cover.
Many sewing machine stores also offer free and paid lessons. You may want to sign up for these to get to know your sewing machine a little better.
Follow all these suggestions and you will walk out of your sewing supply dealer with a great sewing machine for a beginner to learn on.