If I saw a fitting going on at a range, I would do it! Thats the best situation. You can try something out, and you might be able to get a feel for the different clubs out there.
Everyone should have a fitting once, just so they know they arent using club specs that are completely wrong. For example, if the lie of your irons are off, that could really affect your ability to just hit it straight.
Shafts are a big factor, but I would say to err on the soft side. Softer shafts make you swing slower with good rhythm.
As far as grips, try asking the golf shop to add an extra layer of tape or two (or three) during a grip change. Try it out.
If you are using the wrong club setup, you should see an immediate improvement.
If you dont see an improvement, then you know you gotta work on swing mechanics.
Either way, its good.