What you are looking for require little customization, but it all depends on how you plan your website, when you said "What comics they have and witch one they dont have" this means that you should have a complete listing of comics book and users will have to select from this list which ones they do have, and everything else will be kept into "Dont have".
This is quite confusing as it might lead to 100's of Dont have, what i suggest, is users will include comics book they do have and post it at their profile.
You should consider couple of components when you plan and engineer such website :
a. Community website
b. Indexing solution
Community component is used to have profile of users registered in your website and include all their commics books details in it.
Indexing Solution required to post the long list of commics books and maybe orgenize them in different categories.
try the following components :
1. Indexing component : "Mosets Tree" http://extensions.joomla.org/extensions ... ectory/233
2. Community component : "Community Builder"http://extensions.joomla.org/extensions ... nities/210
Community builder having many tweaks, additional modules, plugins that will enable you to customize it toward your website requirements.
My final suggestion is to plan your website properly before start developing your website and list your exact requirements accordingly look for the right solution that match some or all your website requirements.