Generally speaking, routers use either the 802.11g or 802.11n standard (if they use N, which is faster, they also support G). Any router using 802.11g will be able to talk to any device that uses 802.11g, regardless of whether or not the device is "supported" explicitly -- both devices use the same standard, and it's called a standard for a reason. The truth is, the router doesn't really know what OS is being used by the device -- doesn't know and doesn't care, so long as the standard is implemented properly by the device.
802.11n is slightly more problematic, but any router and device sold in the last year or two ought to work fine, though there are potentially issues with the band that they can use. Generally, a plain-vanilla N router and a plain-vanilla N or G device ought to work fine. You can spend extra money on "dual-band" N routers, but unless you have a dual-band device to connect to it, you're wasting money and electricity on a feature you won't use.
Now beyond the N or G question, is the security issue -- unsecured, WEP, WPA, WPA2, and so on. You do need to make sure that the security option the router uses is supported by the device. WPA2 is generally the modern preferred choice. I suspect any new router you purchase today and any new device you purchase today will support WPA2. Set up both to use WPA2, when presented with a second choice just pick one that appears on both your device and router (you might see a choice like WPA2-TKIP, for example -- what the TKIP means isn't important, so long as both devices support the alphabet-soup choice you make). Finally, choose a hard-to-guess password (a bunch of random letters/numbers is ideal), enter the same password on the router AND the device, and you're done. Some routers offer more choices beyond that, and a networking guru would worry about more options, but for the home user that's pretty much all you need to worry about - use the default options for the rest of the setup and don't sweat it.
Yes, there are issues where one router doesn't work well with a particular device. Those cases are rare, and usually indicate a poor-quality router or is really some other problem that's manifesting itself (inadequate power supply, radio interference -- these are radios, and things like microwaves and cordless phones can interfere with their operation).
In other words -- ignore the list of supported OS's on the router's box. It doesn't really mean what you think it means. Pay attention to the N or G designation, the security options supported, and for an N router the band it uses (which you can usually ignore unless it talks about "dual band").