You pose a sort of difficult to answer question.
Let me try to break this down a bit. That may be a RT2870 Wireless chip. Not an easy chip to get working I believe.
Second is that browser linux. All of the specialty type distros tend to be more difficult to get working. Source code tends to need many other files and programs. One of the reasons it is small is because it doesn't have all those extra files.
It may be easier to buy a common supported usb wireless nic.
As to this distro, we'd need to know more about it. What is the base, for example is it a debian or what?
I might be tempted to try some of the other made for old system distro's before I put too much work into this linux.
DSL is still a good choice and still made for older hardware.
Xpud might be a choice too.
Austrumi might work.
I like Slitaz no matter who says what about it.
The only limiting issue with the 256 is that you might be able to get some of the ones listed at www.distrowatch.com
to work by selecting one of the alternate choices of window managers. Some of the common distro's offer a choice that may work on this system.
Other choices might be Vector, Antix and even Slackware,
Try Slax too maybe.