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A couple other people have asked a nearly identical question in the past. Sometime I will have to compile the answers and put together a "chainsaw on a budget" webpage or something. But for the time being, a summary:
$200 is a popular number for a first saw, but it creates a couple challenges. First off, it is just a hair under the price at which you start (and just) to get into the realm of a small all-purpose saw. The saws you'll find at this pricepoint are usually very small saws, suitable for small trimming and limbing, but not particularly well-suited to firewood duties. If you can get by with them, though, then this isn't a problem.
Second, you NEED to factor in another hundred bucks for an extra loop or two of chain; files and a filing guide of some sort; bar oil and mix; and most importantly SOME DAMNED PROTECTIVE GEAR! I know I've had my close-calls and a couple little accidents and it scared me straight. By way of a more dramatic example, the older guy who lives across the street from my parents was kneeling on the ground flush-cutting a stump with an MS210 earlier this year and it kicked back and went straight through his jeans and into the meat below his kneecap. Suffice it to say, I bet the cost of those "expensive" saw chaps now seem like a worthwhile expense. OK, safety lecture over.
OK, back to your question: what to do? Assuming you're settled on a new saw, I'd get some proper protective gear and a good, LIGHT, inexpensive saw. If, down the line, you decide that you need a bigger saw, then you'll already have a little saw for small tasks and as a back-up saw.
I'm a big fan of the little old-style Echos (30x and 34x series), and you can get them at good prices new-in-box on eBay, especially on the CS346. With a few corrections for what the factory did wrong and a bit of opening up of the muffler, they are a heck of a value. They are not the fastest saws around, however they're durable as can be, tolerate neglect well, and are LIGHT!!!!! The rear-handle saws are better all-around machines, but I put this one together for about $200 net of buying a new bar/chains/tensioner and reselling the INTENZ bar and chain that came with the saw on eBay.
The little Stihls are also good saws, though they're not as light as the Echos. They're surprisingly peppy cutters with their narrow chain, though it is somewhat harder to hand-sharpen those mini-cutters than the cutters on regular low-profile 3/8" chain. I've used a couple MS180s before and have been pleased with their performance in smaller wood. The 210 is a decent little saw, too, though it is bigger and heavier.
If you have the patience and if you're comfortable buying used, you can get a lot more saw for your dollar in the form of a good used saw. I picked my current Stihl 026Pro, pictured below, up for about $200 from another arboristsite member. It has been a flawless performer and it is a LOT more saw than anything you could buy new for $200. Similarly, I recently sold a very clean 026 that I didn't need, along with a new Stihl bar and chain, for a hair more than your present saw budget. So unless you're intent on buying new, I'd give some consideration to a quality used saw.
