Can anyone advise a router to setup a FTP server?

My problem is that have an ISP connection without a static IP address. I have previously setup an old computer as an FTP server running a No-IP client, with Port-Forwarding setup.
I now want to get rid of this ugly computer and get one of these new Network Storage boxes that can act as a FTP server. I understand that I will need to get a router that supports a DynDNS service like No-IP in order to do this - since obviously I can no longer use the client. Can anyone recommend one? Do they work? Does anyone have experience with this?
Any advise would be greatly appreciated.

Thanks for that Riser.

I checked on the Linksys website and pulled out the manual. It seems that it only supports www.dyndns.com and www.tzo.com. Has anybody used these before? Do they have a free service?

I also saw Planex (PCi) routers does the same thing, though it doesn't say on the manual which services they support. Anyone have one of these? Out of the two brands which is better?

I dont know if your router will have this feature like mine (which is also a linksys but i dont have the model since i am at work) but I can set the router to grab the same IP every time through the modem just like connecting your nic to the modem. But really it shouldn't be that big of a deal if you dont turn off your modem. And for the network IPs you can setup ip reservations by using mac address filter, and then just set it to forward the needed ports to those IP's and never deal with it again.