slackware is difficult cause it doesn't use dependency chains, you prolly don't have all the needed installed software to run wine correctly.
slackware are for really really into linux users. if you want a light weight Linux, that might not demand as much from your system, you can give arch linux or gentoo a go(these are not for the beginner either, give ubuntu or fedora a walk around the park for about six months then move on, arch has precompiled packages that you install what you want, where gentoo, you compile it all from scratch from a command line, it can be daunting.)
most people will be forever happy with ubuntu/linux mint or fedora, the other distro's are for ppl who really want to understand how linux works, buidl their own and what not.
hope you have great success, you will love ubuntu