Indeed, it is easy enough (and more cost effective) to upgrade one step at a time
Any one part of the upgrade can make a marked improvement in sound quality, but only once everything is done will you really see the full benefit.
Myself, I changed out the head unit only and left the remainder of the system OEM. Noticably better sound, but now the HU is putting out far more power than the crappy 17 year old OEM speakers can handle. They are living on borrowed time before they blow completely, and I expect to have to upgrade them before too much longer.
Whether or not you change one component at a time or all at once depends entirely on what you are trying to achieve and what your budget allows. Regardless, I strongly recommend you buy the best quality you can afford, especially when it comes to the head unit, and any cables/interconnects you add.