It may help to direct the replies if we can clarify one or two questions that come to my mind, at least.
Firstly, do you "want to make" or "need to own"? That gets the make or buy question out of the way.
Next, is "small and compact" really important to you? (Sounds like it is.)
Lastly, what about budget? How much are you willing to spend?
If you want small and compact, then a linear supply is likely not going to suit. It will be big and heavy. That would leave you looking at a switch mode supply--not perfect for everything, but good for many things.
Variable voltage switch mode supplies are hard to design and build. Most design guides ask you to pick your output voltage and work backwards. If your output voltage isn't fixed, you get into uncharted territory.
Have you considered one of the variable voltage regulated DC power adapters available as a wall wart? One of those could be really handy in your circumstances.
A more complicated possibility is to use a laptop power brick as the main supply to a linear variable regulator in a separate project box. Most laptop power bricks supply 19 V at 5 A or more. They make ideal isolated supplies in a nice form factor.