http://www.no-ip.com/downloads.php There's the direct download link, sorry.
It is almost always better to install from your distro's repository, if it supports the package in question. That way the installation (and any dependencies) can be handled automatically by your distro's package manager. It looks like Ubuntu supports no-ip, so your best bet is to run "sudo apt-get install no-ip" instead of downloading and installing it manually.
The dynamic ip have nothing to do with the OS you run.
Just get a router capable to update a DynDNS account or a similar service.
Next, set the router to route the traffic on ftp port and http port to your server.
Seems kind of silly to buy a new router just for this. DynDNS also recommends against using router-based update clients
, for a variety of reasons.
If the world isn't making sense to you, you're either drinking too much or not drinking enough.