Yup, the Shimano site will tell you all about compatibilities.

I run the 9-sp Shimano grouppo on my bike. Having ridden in PA for a few years, I would make two recommendations. The grades will be similar. One, I would avoid a triple. Two, I would keep your chainrings and change out your cassette with the largest gear you can get.

I began with a 52-39 chainring and 11-23 cassette bike from South Louisiana in the PA hills. It was tough but I hung with it.

I then tried the triple and cable tension was always an issue as were the adjustments on the derailleurs. So I decided to get a larger cassette for the 9-sp and wound up with a 12-27 cassette. The steepest grades are OK with the 27t gear on the back.

A compact will make it more difficult to gain high speeds on the flats. So, if you are going to ride flats, you will be glad you have the 53 chainring.