Usually most hardware is supported in the kernel. You should do some research to see if anyone has had problems, but in general it should be fine. You should however research graphics cards, printers and scanners for Linux compatibility. Drivers for other distributions *can* be made to work with Slackware (I repackaged Brother's debian package for their printer drivers [sadly they have no 64-bit drivers]), however this isn't always easy and unless you repackage it properly and possibly adapt the init scripts you may get things placed in weird locations.
I have built two computers and did not put much thought into Linux compatibility for either one. Both are fully supported by the kernel (though I used nVidia's proprietary drivers for the graphics card), and three older prebuilt computers have also been 100% supported without me researching Linux compatibility. I also have a Firewire card and an SATA RAID controller card that worked fine.
Basically, you should do some research but unless it's a printer, scanner, graphics card or something more obscure (a tablet perhaps) then it will likely work, as long as it isn't bleeding edge new.