Warning: I had coffee after dinner. No sleeping for me, so this turned into a book. I'll highlight the important bits in case you want to skip the commentary.
First thing I would do is just play with the machine. Get some cheap fabric (no slippery stuff, no velvet, nothing too stiff, stretchy, or sheer) and make some rectangles. Then stitch the rectangles into pillow cases (not necessarily as large as a regular pillow). Turn them right side out, and look at your stitches; if they look wonky or pull apart easily, or you get a mess on one side of the fabric, get someone to condition the machine for you (clean, oil, set the tensions, etc.). You do not want to try to learn to sew on a problem machine.
Once you are happy with the machine, there are a few things you will need to get started.
Scissors: get a nice pair of approx. 8 in. bladed ones (maybe $20 to $30 dollar range - better yet, check for sales at your local big fabric store or use a coupon so you can get those nice ones for about $15). Now HIDE them. Do not let anyone use them for anything other than fabric. Write on them with a permanent marker, tie a ribbon on them, heck, buy a lock for them, do whatever it takes. Using my fabric scissors is a hanging offense around here.
Also get a small pair for snipping threads. These don't need to be expensive, as long as they are sharp. I like the U shaped ones you just squeeze.
Eventually you'll want a rotary cutter and mat, but they aren't really necessary at first. If you decide to do quilting where you cut lots of tiny little pieces, then you'll want them.
Sewing machine needles:
Start with general purpose needles. You only really need the different types if you start doing specialty sewing or using difficult fabrics.
I used to only change my sewing machine needle when it broke. Since I started doing quilting and embroidering, I've learned that a sharp needle makes a big difference. Keep extras on hand so that if your previously well behaved machine suddenly starts breaking threads or making bird's nests you can change out the needle.
Thread:
Buy good all purpose thread. It doesn't have to be the super expensive specialty thread - Coats and Clark is fine. Just don't buy thread out of the bargain bin or at the dollar store. You will regret it. Also if it is shiny or silky looking it is most likely embroidery thread. You can sew with it, but it tends to break more easily - a hassle you don't need.
You don't really need lots of colors to start with (gasp, thread buying is addicting

)- if you aren't going to be top stitching you can get by with black, white, tan, and some primary colors. Once you start making things you really care about, you'll want to match your fabric a little better and fill up bins with your various colors, shades, thicknesses, textures, types, etc.
Straight pins: I like glass headed ones, but the ones with plastic balls are fine as long as you don't iron them. You don't want ones with no heads, they will kill your fingers. And stay away from the cute ones, they often have bad tips and/or burrs or bend too easily. (BTW if you bend one, throw it away. They'll cause you all sorts of problems, and somehow, the bent ones are always the ones you grab first.)
Ok, now some easy stuff:
Vinyl Tape measure, seam ripper (sorry, you're going to need this. We all still do

),
marking pencil or pen (chalk style or disappearing ink), and
an iron if you don't have one.
As for dungarees, it depends on what you mean by that. If you mean heavy denim with a fly, a zipper, pockets and lots of top stitching, I would not start there. If you just mean some easy, comfy pants, that will probably work fine.
Pajama pants, a simple skirt, an apron, or a bag of some kind are some other good starting projects.
The patterns you can buy at the store are often complicated and use jargon that they don't explain. Patterns you find for free on-line sometimes are sketchy and leave steps out. I hear lots of good things about
youcanmakethis.com Clear instructions, lots of pics, and a bit of humor. They have some free ones you could get started on; then if you like the way they do patterns, you can go for something a little more advanced.
Have fun and post some pics of what you make!