I'd suggest looking at existing designs, given the limited budget you have. Experimenting takes money: fi. you need parts to test and adjust the filter.
Given the budget you're likely looking at simple designs, like the ones using Tangband or Omnes full range speakers. The magazine Klang + Ton has several simple designs in their CT series of articles. F.i. the CT 222 would be a nice fit given the included woofer design.
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