Great question. Honestly, I don't believe a compilation exists that focuses exclusively on '62-'64. Which is too bad, because it would serve a purpose, as you have illustrated. A lot of people distinguish between the '62-64 and '65-66 material. The earlier albums
are uneven. The closest thing to a pre-Today! comp would be disc 1 of either the Good Vibrations or Made In California box sets, but obviously, that's not an option (nor ideal). I tend to agree with Cincinnati Kid that Endless Summer and Spirit of America may be the closest you get, but there's a lot of overlap with Today!/Summer Days. I'd suggest listening to the earlier albums on Spotify and deciding to buy albums that way, or even making your own playlist on Spotify of your favorite early material. You won't get much of a consensus around here (outside of the hits), but there's a lot of good music to find. Again, I agree with Cincinnati Kid regarding All Summer Long. 10 very good to great songs on that album alone.
Edit: Actually, here's your best bet
https://en.wikipedia.org/wiki/The_Original_US_Singles_Collection_The_Capitol_Years_1962%E2%80%931965. You can get it on itunes for $30.