I am building my first computer with an ASRock Z77 Extreme4 motherboard. I have an old mouse and keyboard from a six year old computer that has round connectors that plug into the computer/motherboard. Will these work with this build or do I need to acquire mouse/keyboard with USB or other connection?
Those are old PS/2 Connections. Most motherboards come with those types of connections, but I would highly recommend getting a USB mouse. You can find them almost anywhere. Be it a thrift shop or your friends old one they all do the same thing. If you plan to be gaming with your computer, then i highly recommend getting a gaming mouse. They can also be relatively cheap as well. Either way, you will be able to use your old mouse and keyboard but anyone will tell you that it would be wise to get a new USB mouse. Ask around to some friends and see if they have any old USB mice laying around that you can have (and keyboard).
Best of luck.