Assuming that you'll go brand new, it is best to approach a store and tell them your budget. All stores will have some sort of kit or package that fits your budget. Don't hesitate to tell them that you will be canvassing through all the stores and don't hesitate to show them your choices from the other stores.
Yes, you can have a decent set of cymbals for that budget. Make sure that you don't get a package with brass cymbals, because they break easily. Make sure that you're getting bronze cymbals. At this point, any kind of bronze will be fine... upgrade na lang later if you feel like it. If the store doesn't know what kind of metal their cymbals are, don't buy.
You don't need to replace the skins/heads if they are big brands, such as Yamaha, Pearl, Tama, PDP, DW, DDrum, etc. If they are China rebrand brands (RJ, Lazer, etc), replace the heads, because they sound like [gooey brown stuff] and are impossible to tune. For heads, Lyric has the best prices for the quality (Aquarian heads).