What fertility tests to request

I am 37, healthy and eight months into trying to conceive our first and probably only child. This will come as a shock to no one who is 35 or older and in the same situation. But, it took me some time to meet a man I love who I aso respect deeply and feel confident will be a wonderful father. 
​The one upside -- we are very informed about our bodies and have done a fair bit of research around conception. On Friday we have an appointment with my OB/GYN.  
​Are there any particular fertility-related tests that we should request? Are there tests any of the ladies over 35 wish that they had undergone sooner? Are there any tests that provided particularly helpful information that we should request?