Three chords, indeed, should get you on your way -- you can play *lots* of songs in one given key. G/C/D, as suggested, gives you a fairly complete "set" of chords for key of G -- and it also gives you 2/3 of the chords you'll need to play in either of two *other* keys: add the A chord, and you have the three chords you need for the same progression in the key of D (D/G/A), and add the slightly-more-difficult F chord to play in the key of C (C/F/G).

It would be good to quickly get a sense of how to transpose -- how different groups of chords provide the identical (maybe "equivalent" is a better word) progressions in different keys. However, it would be even better to become able to start playing familar songs, songs you enjoy, as soon as possible -- even when you can only do it in one key.

If you can just get to a point where you are able to play one or two songs that you really enjoy, you'll be much more likely to log the necessary hours to build muscle memory and calluses, and thereby become able to take the next step and the step after that, etc.

That slightly more complicated 4- or 5-chord progression Leadfingers mentions (C/Am/F/G-and-or-G7*) works not only for "Diana," but for just about any "slow-dance" tune from the early rock n roll era, and a lot of uptempo doo-wop tunes as well: "In the Still of the Night" (the Flamingos version with the "Sho-do-bin-doby-do" backing vocal, not the Cole Porter standard) and "Runaround Sue" are just a couple that come to mind.

*I don't think that G & G7 are necessarily different chords in this context, i.e., when they're the VII chord and when the player is a beginner. They're essentially interchangable, and you don't need to know both. Maybe it's a four-and-a-half chord progression.