BTW/FWIW. There ARE some considerations based on the frame's geometry, primarily the head tube angle, which may need to be considered if you are really optimizing your riding position; so, excluding those considerations, and working only with the arbitrary ...
Perhaps mostly based on MY aesthetic sensibilites (or, lack of), unless you are over 6' (183cm) tall, I think a stem longer than 120mm generally looks too long ... that is, if the top tube is only 56cm (for example), and you opt for (find you need) a 13cm stem, it is probably a frame that is a little too small & you will probably want to consider a slightly larger frame ... in part, the stem length will affect your fore-aft "balance" on the bike.
At the other end, if a stem is shorter than 85mm (?), it probably looks too short unless you are riding a DH bike OR you are really short and can't get a smaller frame OR you/whomever are more comfortable with an upright riding position ... that is, if the selected stem is really short, the frame may be too large for the particular rider.
BTW/IMO. The "problem" with an in-store fitting is that UNLESS you are going to sit on the gizmo for one-or-two hours, it may not give you a sense of how you will feel when you are on the road for a couple of hours ... of course, the fitting will tell you what positions don't feel good; but, that could change over time. AND, conversely, what feels great/good/"okay" could conceivably be a disaster in the future ...