It won't be easy to deal with all these files. Combining, minifying and compressing all these together will most probably bring issues. It will take much effort and a combination of techniques to reach a satisfactory optimization level.
My overall Approach to achieve a fast loading site.
A fast website is essential. The speed optimization of a website, although it usually takes places at the end of the development, it is something that should be considered from the beginning. It starts with the proper template.
Also installing each and every extension, and using any kind of fancy modules, it probably result to a heavy website, that will be very hard to make it lighter later on.
Be eclectic - stay minimal
Personally, when it comes to speed optimization, I try to be very eclectic on what extensions I use. I research and experiment for the most efficient and quality ones for each task, and always try to avoid to use any extensions, if there are things that can be achieved manually within the core.
Also, if I have to decide on using a fancy front-end feature not really important, that causes me troubles in speed optimizing the website, I usually will throw it away, or find another way to implement the fancy feature.
I also try to avoid to use commercial templates, since they usually come with many extra features to satisfy many different tastes. I prefer to build the template and include only what I need.
Your Manual Work
I would suggest to review all the extensions you have to see how they load their assets files, and if it's possible to avoid load them in pages where you don't need them, e.g. you could create template overrides where possible to control on your own the loading of the assets files.
You might find that there are extensions that you don't need, but are still loaded, or you don't have the optimum settings on how they should work.
E.g. JCE Mediabox provides option to be loaded only in specific menu items.
Also see if it's possible to merge files in one. E.g. don't let any module to load it's css, try to merge it with the template's css file.
As for optimization tools/plugins, I am pretty happy with the JCH Optimize plugin. It's free, but also has a commercial version with support for a few bucks. With the proper tweaking, it can produce great results and the developer is quite helpful if you need support.
I also use Jot Cache, to have better control over the Cache, since many extensions have issues with the core cache.
Using CDN to deliver static content is the next tool - I use NoNumber CDN for Joomla
Finally, big benefits you will gain by using an htaccess to compress and add Expire headers to the files.