Hey mate
Congrats i can relate ro your excitement.
Only bought my first boat two weeks ago. Spoke to plenty of marine mechanics and they all said a compression test and a good run with plenty of WOT will highlight any issues. Comp test is easy as and takes ten minutes.
Obviously just test everything including tail lights, nav lights, sounder, radio etc as these little things add up to a nice bill if you have to repair.
Good luck.