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You can do it either way.
If you already have clubs, you can get a static fitting. The filling will check the length of your shafts, the lie angle (not same as loft), and your grip thickness. If your clubs need adjustments, the fitter can do it, but each thing he does will cost you some money.
Also, you can get on a launch monitor to see how your clubs perform for you: Is the shaft and head combination what you need for your swing?
If you get measured first, you can start out on the launch monitor and use your current clubs to get baseline data on your swing. Then, you can test out other head and shaft combinations to find ones that will work for you. If you buy a new set of clubs, the fitting should be free.
A full fitting works best if you have a fairly stable swing. If you hook the ball on Tuesday, and slice it Thursday, and do both Saturday, a full fitting won't help much - you swing differently each day. A static fitting on your current set would be best in this case.
If you are becoming more serious about golf, you might combine lessons to stabilize your swing with an eventual fitting. You can figure out which driver, FWs, irons, etc. you need, and then buy them a few at a time as money becomes available.