I will use Linux as base for my simulator software NS2, which version is best and most stable , and which free source can I get it?

Whatever is NS2?

As far as I know, all Linux distros are free, free, free to download. You may pay a small fee if you want them to ship a CD/DVD to you.
I believe you mean 'which distribution of Linux is best and most stable'. Best would be subjective to your wants and need.

If you have never installed/used Linux before, you may want a distro that's fairly easy to install. In that case, you really can't beat Ubuntu's install, pretty straight-forward.

If you are more concerned about stability, then there are several, Debian Squeeze, Slackware and Arch Linux are at the top of my list.

If you want stability with fairly easy install and lots of pre-built packages (software), then go with Debian Squeeze. You can download it from:
http://www.debian.org/CD/

Moved: This thread is more suitable in Linux-Newbie and has been moved accordingly to help your thread/question get the exposure it deserves.

You could start by looking at www.distrowatch.com. For the best to run NS2, I'd google around as well.