Help me buy a bike seat post
Nearly. The diameter does need to match, but you also need to consider the materials -- metal needs grease, carbon fiber doesn't, so combining the materials in the frame and seatpost shouldn't be done. 

Also, note that different seat posts have different levels of adjustability - saddle angle and position, height (which connects to minimum/maximum insertion distance) to name some, so your seatpost will need to be adjustable enough to get a good fit for you.

As for saddles fitting on the seat post, most saddles will work with most seatposts as the rail width on the saddles is essentially standard. 

So, I'd say make sure your seat post is metal if your bike is metal, carbon fiber if your bike is carbon fiber. Then, pick something with the same diameter and enough adjustability so your bike can fit on it (for most people, even a basic seat post like the Bontrager SSR seat post will work fine, though for nice saddles like Brooks, you will want something with a bit more adjustability).