You need to go with a '9 speed' chain because the width of the chain is important. The width limitation is to do with the spacing of the sprockets on your cassette, they need to keep it to that width to squeeze all the sprockets in there. Just out of interest, the 10 speed chain is even narrower again and the BMX (1/8 inch) is too wide. Don't worry about strength, when set up correctly the chain is very strong, somewhere in the order of 10K newtons if I remember correctly.

The length of the chain is also important, the critical factor is to allow sufficient chain so that it will go around the largest chainwheel (front sprocket) and the largest sprocket on your cassette at the same time. Just wrap the chain around the largest sprockets and allow one or two extra links and that's the right length. You'll also need a chain breaker tool to set it up correctly, don't worry they're very easy to use.

I've used 9-speed shimano and sram chains, they're both very good. I also use a wippermann quick release link to easily remove the chain for regular cleaning. Not critical but if you're fussy about maintenance (as I am) it's great.