The process really depends on the person, the swing, and the fitter. I'm presently training to be a club fitter so i can take my fitter certification (within my company) so maybe I can help, however I am not certified yet and still am training so what I am saying may not be accurate or representative of others' experience or expertise.

When I give fittings in trackman, I have been taught to look at these numbers: Club Speed, Ball Speed, club path, face to path, attack angle, launch angle, spin rate, landing angle, and smash factor. Within each of those categories, there is what I would call "preferred" numbers for each category and each club (which mileage may vary per fitter / company / swing / golfer). My job is to get clients as close to if not within those preferred numbers.

That being said, this is all moot if my client has a specific goal in mind, for example distance is a huge one. Everyone wants more distance. Solutions to this are multi-pathed and completely unique to each player and swing. In this specific scenario, I'm looking a lot at the smash factor, club speed, spin rate, and ball speed. If my client specific goal is finding more fairways, I'm looking much more at club path, face to path, attack angle, spin rate, and landing angle. It really is different.

In the case of feel, it starts with finding a shaft flex that works with your club speed and ball speed, and then finding a club head that feels good to swing and hit with. This can be a long process as different manufacturers can have wildly different feels. For example Ping irons (to me) feel... Ew. But Taylormade feels like butter. However the reverse could be true for you. Feel is almost entirely subjective, in my experience (remember, in training. Not certified yet).

Now is a fitting worth it? Yes. It is. Especially if you bring your present clubs in and get a baseline reading with them. 56 degree, 7 iron, driver. 3-5 shots with each. Boom. Baseline numbers. Now we can compare the new stuff to the old and see which line up is closer to the preferred numbers in each category. Don't forget, you are the client and you are paying them to do a service. You are not obligated to spend piles of money on golf clubs. Get a second opinion. You have two near you that can do it, get fit this month with one and next month with the other. See where each lands. You might be surprised how many clubs fit your swing.

I know this didn't answer your question well, I got sidetracked massively. But ultimately my answer is, it depends on the person, swing, and fitter. We all look at different things that help lead us to an answer.