I just know that with voltage regulators - if you mean basic 78xx type devices (from messing up designing a power supply then having to start from scratch after reading up diligently on the subject) the lower the Vin compared to Vout, the better. Regulators are a grosso modo like a resistor/a funnel, so the higher the voltage/current you squeeze in when you need to get far less voltage out on the other side with pretty pathetic low current loads even, they'll heat up fast, unless you use a bypass transistor and heat-sink where necessary.
You may not find this an issue with a switching regulator. In my ignorance, if that's the design, personally I'd fan the output from one larger regulator to three different regulators (12, 7.5, 5V) so they can do dedicated supplying, to put it that way, and if I understand well a plus is that then you can double filter the switching noise before your respective loads (to a degree).
I'm suffering making a linear supply, and learning about transformers, regulators and variable voltage outputs, and I have to say I prefer measurement devices as they are way less difficult to put together without a lot of important complex issues you must deal with in my opinion, so maybe my advice is not much use, besides Vin - Vout x I = P.
Best of luck!
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Hi again.
TI, and many others, have interesting power solutions, besides some aimed at motor circuits if I remember well. I remembered this from the other day, maybe this type of device or something similar (with a higher current rating) and appropriate to your needs (I'm sure some provide multiple output voltages, like PC power supplies) could provide load current sufficient for the three regulator voltages and current draws you need:
https://www.ti.com/product/TPS54336A/description
or
https://www.ti.com/product/TPS82085/description
The power management section might offer ideas or packaged solutions:
https://www.ti.com/product/TPS82085/description
I know SMPS are supposed to kick back/inject noise into the mains supply, and apparently are uncomfortably noisy on the circuit side, but every problem/issue has a solution, I read that a linear regulator and decoupling techniques remove some of this switching noise (but not much according to a couple of articles); other people with experience in this department will know how to solve that issue with ease.
I stuck to a linear supply as I don't like noise, even if it's unavoidable, and ensuring there would be no mains supply line issues seemed beyond my skill level, but from your choice you are obviously aware that linear supplies have the contra of being cumbersome bricks...
(Disclaimer - despite the appearance, I don't get paid for sponsored TI links, but they do have some pretty nice, small packaged solutions!)