As you suspect, your motherboard needs to stand off from the case or else it will short and everything will explode in a shower of wasted money
If you have a case with pre-formed standoffs, like an iCute case, that's fine. You can tell that the motherboard is in the right position, because the rear jacks will fit into the ATX back panel nicely, and the motherboard will run parallel with the case. Usually, there aren't enough pre-formed standoffs (unless you have a micro ATX case), and you'll need a few of those hexagonal brass standoffs, that should be supplied with your motherboard.
There are commonly two gage of screws inside a case; wide threads for Hard Disk Drives, panels etc, and narrow threads for optical drives, diskette drives. Make sure you use the correct gage for the motherboard; stripped metal can get where it shouldn't.