Paging the list of comments, and getting the comment count
Paging on comments is provided in Drupal Core without any contribute modules. 

If you go to your content type configuration screen:


D6 Path: admin/content/node-type/[node-type-name]
D7 Path: admin/structure/types/manage/[node-type-name]


You will see there's a Comment field-set/tab(d7) with some options. The option you want to check out is the comments per page setting. Select the number you'll like for when a page should break and save your settings. Once you're comment have pass that threshold you will see a pager for your comments.

Now for the comment counts there a variable available to you in both Drupal 6 and 7 in the node template. The name of that variable is $comment_count.