I note that in my city of residence, there are exactly 63 clubs registered on the organization website. How does one go about evaluating the quality of the clubs so as to choose one?
You are always free to visit for a few meetings before actually signing up to join, in fact it’s encouraged. Most clubs have their meeting times posted on the TM website, just stop by and introduce yourself.
In my experience in the Chicago area, the clubs that meet at offices for an hour over lunch tend to be more serious and strict about rules; they have very limited time to get things done, and most people are taking time off work (or using their lunch hours) to be there. The ones that meet in community centers, libraries, etc. in the evenings tend to be a little more relaxed and social because their meetings are often longer and they have more time to chat.
Since most people join Toastmasters to get over a fear of public speaking, I’d definitely try a couple out to make sure you’ll be comfortable with the people in the club.
Yep, what Big_Norse said: pick the clubs with the best location/meeting time for you, and go to a couple of meetings at each club. Guests are extremely welcome, and you will not be put on the spot or asked to speak (except maybe to introduce yourself, but the Toastmaster of the meeting you attend should really take care of that for you) or anything. You’ll find the club that “fits” you best. Welcome to Toastmasters! 
–Misnomer (founder and VP Education of the Technically Speaking Toastmasters Club)
Definitely try several clubs. Each one is different, so you can have your choice. My club is a singles club that is more laid back and we often socialize together. Other clubs are very business oriented and serious with little or no socializing outside of the club. It depends entirely on what you are looking for.