Huge congrats on this acquisition! Lovely piece!
With regards to strap I love bold straps and. If the red goes with your character then it is a superb fit. However I not particularly fond of 20mm straps on Patek with 21mm lugs as they usually have.... sorry that is a no go for me...
I would also venture to say a bright green or even yellow strap would be great. For me personally I would go for calf but that is more to do with my overall preference. Enjoy!!