I'm not a Rolex fan but as mentioned above it's probably a safe bet.
I bought a birth year watch last year and fortunately for me being a Breitling 'fan', they made some very interesting watches in 1969, the Chrono-Matic Navitimer I have being one of them..................
Wow that's nice looking. I've thought about a Rolex but I know literally nothing about them, when I see people talking about serial number for this and that model etc it leaves me bewildered?
Omemga Seamaster 200 is my birth year watch...you could maybe look at some of their chronos but I suspect that you wouldnt hit top end of your budget. May be a Breguet?