First bike build and singlespeed tension problem!

Since most newer bikes have vertical dropouts, people have gotten used to wimpy aluminum skewers, and often don't adjust them as tightly as they might.
If you use a good quality (Shimano is the best) skewer , tightened securely, it will hold just fine in any type of dropout or fork end .
A quick release is a considerable timesaver in switching a flip-flop wheel around, and having a QR means that you don't need to carry a big wrench to be able to replace a damaged inner tube.

sheldon brown to the rescue