No matter what separates you get, you won't get anything worse than Bose. For a budget like you have I would go for what you can get a good deal on, and spend the most on speakers.
OR, if you want separates, try a Parasound processor, their intro model is like $800. You can then get a 5 channel amp like the 200 watt x 5 Anthem MCA 5 for $999 (discounted but that's the going price). You can then get a 5 speakers and a subwoofer for the remaining 3700 - 1800= 1900 right? Go with what fits, I suggest something like Polk (not the tiny ones), Infinity, Paradigm etc...
OR, if you want separates, try a Parasound processor, their intro model is like $800. You can then get a 5 channel amp like the 200 watt x 5 Anthem MCA 5 for $999 (discounted but that's the going price). You can then get a 5 speakers and a subwoofer for the remaining 3700 - 1800= 1900 right? Go with what fits, I suggest something like Polk (not the tiny ones), Infinity, Paradigm etc...