I surf Newegg a lot, and so my recommendation will point you there. Others may have a different approach.
I assume by "normal-sized" you mean an ATX form factor. With that in mind, you'll probably want to be looking for specific case 'types' based on this motherboard size. Try searching for:
ATX Desktop cases. Think like the old Gateway 2000-style cases. Flat, you can put a monitor on them. Although you may severely limit your video card/other accessory options due to height limitations.
ATX Mid-tower cases. You may find something you like there, but for the most part they'll run quite a bit bigger than the next category.
ATX Mini-tower cases. These will be the smallest cases that accommodate a full-size ATX. Again you may want to be mindful of width/height restrictions for aftermarket coolers and video cards, etc.
Another thing to consider might be to step down to a micro-ATX form factor. It's smaller than an ATX but can still have multiple PCI slots to accomodate accessories. The cases above will all definitely fit micro-ATX boards, but there are also variants of all three 'types' above that are specifically for micro-ATX boards, so , think even smaller (micro-ATX desktop, micro-ATX Mid-tower, micro-ATX Mini-tower).