I ride with the local bike club and struggle to hang up with the A riders I'm using a Shimano Ultegra 9 speed . Every one is talking about compact cranks but no one has made the switch that I ride with. My question is the compact crank the way to go? Will it work with my 9 speed and which is the crank of choice

I have one and I like it. Your mileage may vary. It's all about what gears you need. That's a question that only you can answer.

The compact is the easiest thing to change out since you only have to shange the crank and rings. I did that and it helped a bit, but some of the hills where I live in leave me wanting more gear but reluctant to give up my current gear choices, so a triple would have been nice. Problem with that is you need a different derailleur, shifter, and often bottom bracket with that.

What are the A-graders using? If your set-up is about the same as theirs (cranks and cogs), then this is a fitness, power and cadence issue, not an equipment one.

The OP has Ultegra 9-speed so a conversion to a triple would not require a different shifter, 10-speed would.

The idea of a compact is to provide lower gearing for hills but with the convenience and lighter weight of a double as compared to a triple. However, a triple provides even lower gearing and closer ratios.
If you want to go faster keep on riding with people who are faster than you, eventually you'll get faster.

Al