Looking for the best/saftest way to do this. I see several options.
- power module not sure about this
- breadboard with binding posts
- cables plugged in the breadboard rails. Definitely don't like this

I think ideally I want something fixed to the desk which I could use with any breadboard.

Googling relies on knowing terms like binding posts. What do most people do? As always don't laugh, starting out, and thanks.

 

When I play with a new idea I do use breadboard but I bought some of these to connect to a USB adapter... Make life easier.

Search on amazon for breadboard power supply..

I buy these
DollaTek 102 Breadboard Power Supply Module 3.3V 5V for Arduino Board Solderless Breadboard: Amazon.co.uk: Business, Industry & Science

Remember to get the right one.. This is for the smaller breadboards.. there are two widths..

 

The power supply used with one of those fairly standard white breadboards depends very much on what sort of circuits you would be building on it. My preference is to use a small supply that has both adjustable voltage control and an adjustable current limit.
The supply I have for that was a Heathkit that I got at an estate sale 20 years ago, but I think similar supplies are available today. That supply can provide zero to 20 volts at up to about 150 milliamps. This is adequate for low power experiments.

 

power module not sure about this

I don't know what this means. If you have a power supply, why do you need a power module?

breadboard with binding posts

More than 90% of the circuits I breadboard are on individual or combined boards that aren't on a board with binding posts. When I do use multiple breadboards on a board with binding posts, I don't use them 99% of the time.

cables plugged in the breadboard rails. Definitely don't like this

This is probably the most common method for connecting power to breadboards (if wires count as what you call cables).

As always don't laugh, starting out, and thanks.

You're overthinking this. Just do whatever works for you.

 

I prefer using breadboards with binding posts for my larger projects, but I often just use smaller boards with solid wire pressed into the rails.

 

I do most of my breadboarding on a 40 year old Greymark triple power supply breadboard unit. It has built in supplies of 5V, 0 to +16V and 0 to -16V brought out on binding posts. I added some cheap AliExpress 3 digit voltmeter modules to the supplies for convenience. When I use a different breadboard with separate supplies, I prefer one with binding posts because the supply wires between them can not be easily accidently pulled out.
You can build a simple triple power supply using AC mains input to two 24VDC and one 5VDC power modules (again, very inexpensive from AliExpress). With just a few components you can add adjustable linear regulators to the 24V modules to make variable supplies. You can add binding posts to any breadboard by sticking it on an insulated base with the binding posts mounted on the base.
The most important thing you can do to preserve the integrity of you breadboards is to never force over-sized wires into them.