Oh definitely read Strong Poison and Have His Carcase before you read Gaudy Night. Aside from the fact that Strong Poison one of the best of the series, I think one of the things that makes Gaudy Night so rewarding is that you've watched their relationship grow through all three books. And you absolutely can't read Busman's Honeymoon until you've read all three of the others for the very same reason, because it's really entirely about Peter and Harriet's love story, and I think all it's resonance comes from knowing what preceded it.

Reading them in order for the first time is one of the best reading experiences you'll ever have. Have fun! :)