Main synthetic advantage is that it is more water resistant (useful with floorless shelter, condensation or drying wet clothes). Main down advantages is that they are more compressible and lighter weight.
I look at temp rating, compressed size, weight and width/length when comparing bags. Tons of good brands out there. If your looking at lower cost bags, I'd look at Mountain hardware for synthetic and Rab for down bags. I picked up a 5F down Rab bag on outlet for $280 off of Moosejaw recently.
I use both. Synthetic for long hunts, bad weather, and late season stuff. Down for the desert, ultra cold (never get above 25 type cold), and any time I know for sure the weather will be good. Down is great stuff but the reliability of the synthetic is worth the extra 4-8 oz and bulk. I do the same with my puffy jackets.
This does get discussed a lot, and not to tell you to get lost, but rather to give you tons of good reading, try a search on here for "synthetic" in thread title only and you'll get a ton of threads and good reading.
You'll also see a lot of varying opinions with the advent of waterproof down. But in the smallest nutshell, the posts above mine are what you're going to see.
As far as quality, look for the standard things you would in anything else- Made in USA is really cool but there's a lot of good bags made overseas. Get a name brand bag (too many to list) and you'll be fine. Get a WalMart special, and it'll likely be a WalMart special. Not saying you gotta drop huge cash on a bag, but there's a difference between a $400 bag and a $40 bag. Often higher price doesn't necessarily mean better quality, but means lighter and more compressible for the same temp rating and fill. Meaning, a synthetic bag that's rated at 20* and weighs 2 lbs will probably cost more than a synthetic bag that's rated at 20* and weighs 5 lbs but they can both be quality bags. Just that one is for hiking and one is for a float trip.