Data Backup/Storage Using an NAS with Mac OS X and Windows
In order to use the drive for both purposes, you would need to partition it into two. In my breakdown below, partition 1 is for moving data and partition 2 is for Time Machine, but this can be swapped around if you prefer.

I would recommend formatting the partition on which you access data on in ExFAT. It is newer than FAT and does not have the 4GB file size limit. It can be read and written to on both Mac (Snow Leopard and later) and Windows (Vista and later, XP with a supplementary download). This allows for easy transfer between both platforms. 

I would read up on the formats that the router supports, as I cannot access an ExFAT drive connected to it. If that does not work, the best option for connecting from both platforms is FAT, but keep in mind that there is a 4GB file limit.

The other partition can then be formatted in the HFS+J format as Ethan mentioned in his comment. 

In order to get the drive working remotely, I first set mine up on my Mac and started a backup. I then cancelled this and deleted it. I then attached it to my Airport Extreme and then browsed to it through Finder. I needed to access the drive before Time Machine would pick it up (on both my iMac and Air). I cannot say whether the router you link to will work in the same way or not. Please be aware that the way I am doing it is not recommended or supported by Apple and if you do a similar approach, you do so at your own risk.