Best way to stress test a website

Try http://loadimpact.com the best I have found so far, but no alternative to it I can find.

My suggestion is for you to do some automated tests first. Use selenium for it.

Then deploy selenium grid to test in multiple computers at the same time.

Although Selenium as an automated test tool will run quite fast, making a mini stress test. If you put the same automation running on a couple of computers on your network at the same time you'll be able to see how it behaves.

If you want to record response timings, they have a cool api you can use to write some scripts to run your automations.

Edit: Selenium is quite easy to use, and it does asserts to page contents if you want to test the contents. It also copies your movement through the page if you wish (this would be my suggestion) just navigate the page a lot, and then save it for automation. Avoid putting asserts so selenium might run faster.

JMeter would be one such tool. Can be a bit hard to learn and configure, but it's usually worth it.