Phoenix, Firefox is an excellent browser, and it's memory issues have gotten far better then they used to be. I'm curious how long ago you've tried it. At any rate, everybody has their own preferences, and Firefox may not be yours.
Your other options are basically Opera, Safari, or Chrome. If you are on windows I really wouldn't recommend Safari. It was not built as a native windows application, and it shows. It doesn't use the standard windows interface, and thus feels very foreign. I believe it was basically made so windows developers could test applications for the Iphone without needing a mac, as Iphone uses safari. So this rules out Safari.
Opera is a great browser, and is known for innovating. They were the first browser to support tabs, for example. I can't exactly put my finger on it, but something about the browser feels 'different' and 'out of place' to me. However I really can't think of any concrete things to say bad about it. So you may want to give it a try, you may like it.
Finally, there is Google's Chrome. This would be my first choice for you. It is a lightweight browser, and it is extremely fast. Google is great at simplicity, and only showing you what you need at the time. I only have one complaint against Chrome for normal browsing, and that is I hate the way it scrolls. It seems way to fast for me, and I haven't seen a way to slow it down.
Well thats my browser rundown, I hope it helps. I personally use Firefox, mainly for the developer tools. Firefox is by far the most extensible browser, and you can tweak it and add functionality to it to make it fit your needs. However many people don't need all this extra functionality, and I am guessing you may be one of them.