Best testing tool

There are lots of good tools for performance and optimizing, and Michael-Best  mentioned some good links. However, the best tool for UX and usability testing will always be human beings. A tool might give some tips, but it cannot tell you WHY something isn't very usable.

Honestly, your best bet for those two things is to get a good book or two from Amazon on the topic of usability (Jakob Nielsen is a good author in this area), read through them to understand good principles, and see if they apply.

Alternatively, you can try to hire a consultant to give you feedback, but if you don't know any better yourself, then you might just be throwing money away on some person who thinks that usability is the same thing as good aesthetics and design. A GOOD usability consultant is going to cost you a lot of money, and it's ALWAYS better to actually understand the principles yourself, since it will benefit you in many different ways.

In a similar fashion, accessibility tools might help you find problems, but the tools and tests really need to be executed by a human being who understands how the site SHOULD work so they can compare and see if it actually works as designed. For example, JAWS might read you all the content on the site, but you need to actually hear it and compare it to the -intended- content to see if the visually-impaired are missing any messages (like an announcement that is presented as text inside of an image).

You can see top functional testing tools evaluated by real users on IT Central Station here http://www.itcentralstation.com/categories/functional-testing-tools

This Senior Automation Engineer uses HP LeanFT because, "In our case, because we’re in the insurance industry, we have technologies from 20 years old to brand new. That’s one reason that LeanFT is so great -- because it can support all those technologies, even the older ones."
You can read her full review here: http://www.itcentralstation.com/product_reviews/hp-leanft-review-33060-by-sharon-greene