http://www.iwata-medea.com/products/...es/bottles.jsp
I have a friend who loves the Fast Blast style caps for his Badger, since it's just a straight piece of tubing for the paint to flow through.
The medium for thinning the paints depends on what type of paint you are using. For lacquers and enamels, there are specific thinners for each kind. For acrylics, you can use a number of products, but you'll have to experiment to see which works best.
Some products I have seen used for thinning acrylics are that brand's thinner, isopropyl alcohol (91% is basically Tamiya's thinner), and regular or distilled water.