You can make use of jQuery in your case.
Difference between jquery and jquery.min is that, jquery.min is minified jQuery. Basically minification compresses code. Minificated code is hard to read but it’s excellent solution when you put application in production. It’ll save you bandwidth, your site will be faster and you’ll get better site ratings (on sites like Google PageInsight).

For development, you can go with jquery, because it can make you easier to debug application. When you’re ready to put app in production, it’s recommended to change it to ‘jquery.min`.

jQuery and jQuery Cookie are different thing. The thing you mostly need is jQuery, it’s here to help you write JavaScript code for various things, HTML/DOM manipulation, CSS and much more.
jQuery Cookie is 'jQuery plugin’ that’ll help you manage Cookies in browser. Cookies are here to save needed informations, like which user is logged in, some user preferences and similar things. It’s pretty useful if you want to use cookies.

About jQuery communites, you can even try asking here. The biggest community, where you’ll find all answers is definitely StackOverflow. It has answers for almost all question you have. For fastest answer this is probably best place. There is jQuery Forums and jQuery IRC channel, but I’m not sure how fast you’ll get response there.