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Assuming your question is legit --
I am no expert on Bose products, but a quick internet search told me that you have a 5.1 system with a powered subwoofer.
The unpowered small speakers are nominally 8 ohms and the recommended amplifier power is 10 watts. This suggests that your system is compatible with almost all 5.1 home theater receivers.
The limiting factor in your audio fidelity is likely to be your Bose system, so you may choose not to spend a lot on the other components unless you think you might upgrade later.
I am really not familiar with the specific receivers available in your target range. Perhaps some other members might recommend specific receivers that they think you will like.