zedek - it's not so much hard as you just want to worry about consistency and compatibility. is your case already ATX form factor? if not, your mobo may not fit in an ATX case, and the power supply connection may not work.
in that case you'd want to buy a good AT case. but i doubt that IS the case. when you move parts, it's fairly easy. most stuff can't be plugged in wrong anymore, and almost nothing can be plugged into the wrong place (all the different cables are all different sizes, making it pretty straightforward).
really the only thing is remember each drive needs power and data connections, and that your floppy drive is the only thing that can easily have its bus cable plugged in upside down (resulting in constant-on floppy light when you power the machine up; easy fix).
try to put your expansion cards back in in the same order in the new case, because some motherboards are picky about what onboard items share resources with slots and some things just don't want to share system resources. so if it works now, remember (or write down) which card goes in which slot. i find the easiest way to do that is to use a sharpie and put the slot number on the top part of the expansion card anchor rail before i remove it. mine are all numbered; i practice what i preach.
anyway, just take your time, make sure standoffs are in the right places on the back of the case, and screw the mobo down; you'll do fine.
~ dan ~