I'm new to sewing, and I don't know what sort of things I should watch for when buying a machine. I also don't know what kind of price I should expect to pay if I want something that's good enough to last me a long time, but doesn't have gadgets I don't need.

I hope to use it to work with cotton and linen primarily if that helps.

Thanks!

http://www.cet.com/~pennys/faq/smfaq.htm

If you're on a budget, I'd suggest a good used machine — the cheapest new machines are often unrepairable, and are so persnickity about adjustments that they can be incredibly frustrating. I'd really sooner see you with a machine with some scuffs and nicks and only a few stitches that won't frustrate you. When you outgrow the machine, you can always trade it in or keep it as a backup machine.

Things I want for a beginner to have in a machine:
— very good straightstitch
— good zigzag — 4 mm is plenty wide enough for most purposes.
— a method of making buttonholes that isn't frustrating (automatic buttonholers are easier than 1 steps are easier than 4 steps, are easier than buttonhole attachments like the old Greist attachments — however, the Greists made very nice (though limited sizes) of buttonholes)
— adjustable presser foot pressure

Nice to have, but can be lived without:
— three step zigzag (great for elastic application)
— blindhem and stretch blindhem stitches (saves hours!)
— a few decorative stitches (just for fun)

If you've got the budget, I'd suggest considering an electronic machine — they don't stall at slow sewing speeds the way many mechanicals will, and they sew very nicely.

I'd also send you to a real sewing machine shop… several, if possible. Tell them your budget, that you're a beginner, and ease of use and quality is more important than all the bells and whistles. Ask to see machines in your price range, and also ask to try a couple of good quality machines outside your price range so you can see differences in quality of stitching and ease of use. (Elna, Viking, Pfaff, Bernina…) — not the embroidery machines, ask to try one they might sell to a picky person who has a separate embroidery machine.

There are quite a number of pre-loved machines around, many of which are sitting on shelves in repair shops, taken in on trade, overhauled, and ready for a new person. There can be some excellent values there.

Always ask (new or used) who will service the machine, what the turnaround time usually is, availability of parts, can it be done locally, or will warranty service require it to be shipped off elsewhere.

Suggested reading:
John Giordano: Sewing Machine Book
Carol Ahles: Fine Machine Sewing (especially the first and last few chapters on care and feeding and selection of sewing machines — also skim the chapters on hemming.
Gale Grigg Hazen: Owner's Guide to Sewing Machines, Sergers, and Knitting Machines

Your local library is likely to have both books on the shelf.