Your motherboard is the IPM87-MP (Pegatron-made for HP PCs). It is micro-ATX (mATX) in size measuring 9.6" x 9.6".
Any ATX case will surely fit that motherboard of yours with some "void" space below it. You can also get an mATX case that will snuggly fit your mATX motherboard. No worries in "flipping the board" as the screw holes should be standard in any case you will pick (note that there are some cases that also have the same inverted orientation, while most cases have the regular orientation).
The choice of the case will generally depend on your other components that you have (such as GPU length clearance, PSU size, CPU Cooler height, number of 5.25" external drive bays, 3.5" internal HDDs, and 2.5" internal SSDs. Other features such as windowless (silent) or window (show-off internals), front panel USB ports, aesthetics (color and looks), and airflow/cable management also come into play in selecting which suits you best. Lastly, the budget.
As you did not mention any specifics, here are some good cases that will fit your motherboard: http://pcpartpicker.com/products/case/#f=7&p=0&sort=a8&R=5,4&t=3,2,7,6