Some models have a hole, some don't. I have two of that basic type which do have a hole. There are varying opinions as to whether an autoharp needs a hole for 'better' sound. Personally, my old ears don't hear minor nuances in sound. The hole does serve as a place to put identifying stickers... but it's also a place to lose picks. *wry grin*. I moved 40 years ago to the 21 bar 'harp, but still have a couple older ones of 15 and 12 bars which I seldom play. (I also have a model of the original Zimmerman 'harp from about 1900... with shifters.. that I used to play, but which needs some repair because of the older type of glue used.)
   The important things about getting along with it/them is accurate tuning and choice of picks. *IF* you want to get fancy sometime, I recommend some type of pick that you can strum either up or down... basically a wire or solid brass triangle like a Sitar plectrum. Until then, plain plastic picks will be fine. (metal picks are much trickier, as they can more easily get caught and pulled off)
   Yes, some folks still like to play with it laid flat on a table or on one's lap... but held to the chest is much more common.
Watch videos online of various people playing and slowly decide how YOU prefer.