Most of the time you should pick for the customer, otherwise, you end up with Times on a coro
sign. For occasional use with walk-ins and quick jobs make a large banner with 20 to 50 fonts divided into sections by style and let them pick from that. Looking through 1000's fonts will just waste everyone's time and confuse them. On the same
sign or banner, you can illustrate the sizes of banners and letter heights. If you place it a the back of your shop, you can also illustrate letter height and style visibility from a distance.
You design and make
signs, why not used them to your advantage. Anything that can help educate, and direct the customer makes you look knowledgeable and professional, and the quicker the layout gets done, the more profitable you will be.
Designing a logo from scratch is an entirely different process and they probably shouldn't be picking the fonts either. You should pick several fonts based on the message the business is trying to convey; whimsical, strong, bold, modern, minimalistic, retro... and, easily readable font/s for secondary or tertiary messaging.