You're probably going to get more opinions than there are machines to be opinionated about, so you get to pick! (what fun :-\ ) So here's my US$.02 worth...

What You Need:
Straight stitch, reverse (you flip a lever and it sews backwards, for locking down the ends of seams etc.) and maybe zigzag. (It will probly have zigzag unless it's one of those old-fashioned Granny-Had-One types. Those are great, but most are "antiques" and priced like it.)

Get a good brand, just-the-basics machine, either new or used (see below). I can't give any advice on buying new machines, since I never have.

If you decide to look for a used one:
First, find a reliable sewing machine repair shop (not just that guy that shows up at Jo Ann once a week, and not your local Fixitall shop where you take your toaster). And find a friend or two who sew to go along when you shop.

Then keep an eye on 4-sale ads, garage sales, and thrift shops. (I've bought 2 old-reliable type Singers for less than $20 at thrift shops; both were missing footpedals.) Expect to put another $30-$75 into it to get it tuned ($25-50) and any repairs done, or parts replaced.

Make sure it's a name brand and make the seller let you plug it in and try it. (Might not hurt to get some needles and scrap fabric to take with you.) If it will stitch, take it straight to the sewing machine shop (better if they're certified in fixing that brand) and tell them to give it a once over. But except for possibly a tune-up, do not let them fix anything without calling you first with the price! (Get that in writing.) Then if they do say major repairs are needed, call a few other places to compare prices, and if it seems in line go ahead.

What You Don't Want:

A serger - they are Not Beginners' Machines, no matter what anyone tells you!

A SuperDuper Souped Up Does-It-All-From-Embroidery-To-Leather-To-Serging type machine - you just can't do everything with one machine; even the mass-production outfits use several kinds of machines for different stuff. These "sew n serge" types do a half-@$$ed job at both. Nor do you want to do everything, when you're just starting out.

One of those $5,000 embroidery machines. Not for newbies.

Low-end brand, low-priced, or "mini-" anything - get a used, or basic new, good machine.

Brands:
Singer gets mixed reviews: my 403 (about my age, all-metal, tan w/cream top) is THE Old-Reliable type. It has zigzag, and cams available for "fancy" stitches. I spent a whole $15 at a thrift shop plus around $45 worth of tune-up/checkout, footpedal, and some doodads. It's great. Even better is the small portable (green) one that says "Rental" on the outside of the attached wooden case (bottom only) - you've heard probly that those cars built to be Yellow or Checker cabs Do Not Die. Likewise, and probly for the same reason, this one. My 1970's Touch n Sew won't - and too expensive to fix. Generally, the older the better.

White seems to get the Wet Blanket in reviews on lists I'm on. Off-brand types may be o.k., especially if they're made for another company by one of the Big Ones (see below). Others but can be hard to get parts for, especially older ones.

Necchi, Viking, Bernina, Pfaff: Rave, rave, rave. These are the favorites of Those Who Can Afford. I wouldn't know.

Hope this doesn't just add to the confusion!

Heather (reasonably happy owner of a small herd of old-ish Singers)