mgattmch@noos.fr has given you a valuable insight. The early mono recordings are incredible. Old Blues eyes voice changed dramatically through the years with his earliest stuff being, IMO, the best. You also get the added bonus of listening to the best big bands in history back the man up. The old LP's are so prolific that they remain very cheap. Go shopping for used LP's if you have a turntable.
Sinatra - good vs great
I don't have a lot of exposure to Sinatra, but my first CD was "The Reprise Collection: The Very Good Years." It's (well, they are) an awesome performance. Even the tunes I don't particularly care for have me tapping my toes. It seems to be very involving. Based on this - I was surprised that I liked it as well as I do - I bought a copy of the Captiol Singles collection. (This is the 4-CD set, not the mammoth 21-CD version!) The new set is nice, but it's nowhere near as involving, and I can't really put my finger on why. Some of the tunes are the same. It was done earlier in his (later) career, so I doubt that it's just that he had "figured it out" - he had long ago done that. Anyone know why this one CD is so much more enjoyable than the other set?