Here's what you must do
1) Concatenate javacript files to minimize the overhead related to file querying (this overhead will disappear with HTTP2 but we're not quite here. Today your page is probably more slowed by the number of files than by their combined size. There are many ways to concatenate files but it should be automated so that you don't have to do it manually every time you change the source files. If you're not familiar with powershell and the likes, dive into build solutions.
2) Don't compress the JS file(s), let the browser and the server negotiate the compression themselves. Any decent server gzip the JS files it serves.
3) Minify the concatenated file. Here again there are several solutions. Uglify.js is both fast and efficient. The minification is a process which consists in removing any useless (for the browser) part of your code (comments, spaces, etc.) and renaming some variables in order to make the code lighter. You'll configure the minification to also produce a source map file which will let you debug in the browser (not quite as easily than with an unminified file but much better than without a map).