Advice on Music

Hi,

This might be a weird question or request but I have been wanting to hear some particular or specific type of music on LP's and am trying to search for them.
I will provide 2 example's of what I am looking for. I don't know the genre exactly but have some slight idea I think.
Kind of looking for older soft vocal music or just music from long ago.

The music would be from the 1940's to the 1960's I think.
First example, Frank Sinatra One For My Baby. I have this album and love listening to this song and the others on the LP but especially that particular song.
Second example, Music: "It's Been a Long Long Time"
I like that really old skool music and songs.

Would that be big band or some other genre?

Obviously Frank Sinatra is one artist that I probably need to get more LP's of if I want that type of music but I am also thinking Nat King Cole, Dean Martin maybe? Not to familiar with artists from those times or the music but I know I like it.

I prefer LP vs CD for this type of music.

Any other suggestions?
Thnx