OK, Yes a linear regulator will provide the lowest noise - as a general statement. No switching so no switching artifacts and that means lower noise.
LDO? Well,
IF, and that is a BIG IF,
IF you can provide an unregulated supply that is just big enough to provide the (Voltage) head room that the LDO regulator needs, then yes, it will waste less power. Linear regulators drop the Voltage down to the regulated value by controlling the effective resistance of the series element (pass transistor or FET). In other words, they turn that excess Voltage * Current = Power, into heat. So the less the needed Voltage drop the less power is wasted. The problem here is if you are designing a ONE-OFF, LINEAR power supply, then you are probably going to have to buy a commercially available transformer. And those
commercially available transformers are only available in a few standard secondary Voltages. So, you are stuck with the transformer output Voltage and then the output Voltage of the rectifier and then the output Voltage of the filter capacitor and that is what you are going to have to send to the the input of the linear regulator. So, if the Voltage difference from the filtered, unregulated Voltage to your output Voltage is larger than the head room of the LDO regulator, that LDO regulator still must drop that full Voltage at your load current. In other words, in most cases, using a LDO regulator does NOT save any power at all.
Now, you can add some other element in the path, like a resistor or additional diodes or whatever you want that provides a Voltage drop, but then you are just moving the place where the extra power is turned into head and wasted. Such additions do not provide any greater efficiency. So "LDO" is not a magic device. It is only a tool that must be used properly. I have designed a number of ONE-OFF regulated supplies and have never saw any advantage for a LDO design. But they were one-offs, not mass produced items.
Designers who are working on power supplies for commercial equipment that will sell in the tens of thousands or hundreds of thousands or millions of units will be able to order transformers made for that exact item, at a advantageous price. They can use a LDO regulator to it's proper advantage by having a special transformer made for their circuit. Unless you want to pay a LOT of money for one or make it yourself, you can't.
The above is why switching power supplies are so popular. If your design criteria calls for high efficiency (low wasted power) then the easy route is to use a switching power supply and deal with the switching noise.
Linear power regulator ICs will have data sheets with design examples. You can follow them - I do.
Switching regulators are available in a wide variety of designs and doing the full design work for each and every one of them is a real PITA. Fortunately, the major makers of those switching regulators have on-line design tools that make the design work simple. Here's a link or two:
https://www.ti.com/tool/WEBENCH-CIRCUIT-DESIGNERhttps://www.analog.com/en/design-center/glossary/switching_regulator.htmlhttps://www.analog.com/en/app-notes/buck-power-stage-design-equations.htmlThere's a lot more available. If you go to a major supply house and pick an IC, they will have links to the data sheet and other design aids.