Hi there people,
great that you, David, are enthused to return to the hobby!
With the arrival of your kit you have now a great range of experiments to do - so you could pick a few and test your ability and knowledge, choosing what you like.
Connecting that idea with the power supply: all the Arduino kits that I have seen with happily run from a plug top power supply. You could be a bit careful about the choice of PSU - the voltage measured by your meter can be misleading as the voltage from some plug packs is not regulated or even smoothed. A 9v DC would be a good start - obviously, one that fits the socket on the Arduino board. There is a regulator and a smoothing circuit on the Arduino PCB. The silkscreen often shows a maximum voltage limitation.
Some months ago I came across a Dick Smith Electronics (DSE) PSU kit (in fact two the same) and started building it as a demo for earlier members of the Electronics Club Altona (ECA). They are 1Amp, 1 to 30V variable supply with current limit. I was distracted and have recently restarted. I have several bench PSUs with different characteristics. It is handy to have a bench PSU to save batteries and charge cells from time to time and also monitor the current drawn but much of that can be done with an arrangement of meters and leads and a few 78XX on a board. etc etc. Current and voltage are often metered on PSUs and for me, the handiest are those with separate meters. In electronics, there are many ways to achieve the same thing. Understanding how and why are the key elements for me. The DSE kits have circuit diagrams and were useful for discussion.
Congratulations on investing in the hobby and a big welcome to the club(s).
As we went along in we produced some Arduino, and some RPI, code that we, I, they played with and upload to GitHub.
Plenty more to write ... later
Mike