I don't think any distro would be better or worse for PCMCIA support. Whether a driver is needed or not will be determined by the device you are plugging into the Laptop. If you are looking to use a wireless card for instance you want one that has native Linux support so you can avoid having to use ndis-wrapper.
I'd recommend a Wireless device that uses the ralink chipset if that is what you aer looking to do. ..
http://www.fsf.org/resources/hw/net/wireless/cards.html
http://rt2x00.serialmonkey.com/wiki/index.php/Hardware
the
ASUS brand ralink PCMCIA card I bought was $25.00 from New Egg.. Took about 2 minutes to get working in Debian.
as for the specs of that laptop you might want to consider a lightweight distro such as Damn Small Linux, Puppy Linux or Vector Linux. or even Debian with XFCE desktop or Xubuntu.
take a look at the
Linux on Laptops website for how-to's for your particular model laptop.
Here are some of what was listed.
# IBM Thinkpad 560 [Slackware9.1]
# IBM Thinkpad 560X [Slackware 8]
# IBM Thinkpad 560x [Slackware]
# IBM Thinkpad 560X [Debian Woody & Sarge]
# IBM Thinkpad 560X [Generic]