It would not be unreasonable to devote half your budget to speakers, since you'll get the most dramatic improvement as you move up in price. Tuners can vary a lot too, and are very sensitive to location, so be sure to test at home. Forgive me for making a non-audiophile suggestion, but in your price range I wouldn't rule out a receiver. I know all the arguments against, but you could save a couple of hundred over a separate amp and tuner, and that'll buy you better speakers that may more than make up for anything you sacrifice in electronics. Also, on your initial budget I'd stay away from name-brand cables. Get your basic system up and running first, then you can have some fun with upgrades later.
Neophite needing advice
Hi - I am looking to buy a new music system (a CD player, an integrated amplifier, a tuner, and good bookshelf speakers), but have very little experience with the equipment part of the project - could anyone recommend a setup for up to $1500 to produce a good sound? I mostly listen to classical music and jazz. Thanks a lot.