I saw a uptime from a Debian system the other day that was over 700 days, over 2 years without a reboot. At least it is stable.
Me, first thing you want to make sure of is that all the software you want is available with the distro. Then make sure it is stable and you can work with it and has good support.
I like Gentoo myself. It is stable when you have it set up correctly, as are most Linux distros. It may be a bit harder to install but keeping it up to date is very easy. There is also the Gentoo forums which are excellent.
There are a lot to pick from. If you have specific packages that you need to know if they are available in Gentoo or not, just post the name and I will see if it is available. I'm pretty sure what you need will be. They have a lot of programs available.
Pick what you are comfortable with. That is key.
Later