Using a large number of JavaScript files should not be a problem, as you can always combine them all together to minimize HTTP requests. Of course, it takes browser time to execute all this JavaScript. There is also a chance that there will be conflicts between all of these JS libraries / plugins or inside the DOM.
As for choosing the right library, it really depends on what type of site / application you are making. If you just want to use ready-made plugins, then there is not much difference in which library you use, and you should just choose the one that has more plugins that you want to use, and I am absolutely sure that jQuery is the best choice here, so as it has most plugins in general.
On the other hand, if you want to write your own components / plugins / code, you should check each of them and see which one suits your coding style and design in the best way. For example, some time ago I discovered that Prototype is better suited to my taste and quite good for large JS projects. But since then, jQuery has come a long way, so I will probably try each of the most popular libraries if I had to create a new project.
Maiku mori
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