Buy, download, move into itunes.
Setting up a google play account doesn't entail buying anything. there's like a subscription thing but i don't use it and you don't have to.
It'll prompt you to buy and you do have to have a valid payment method, but since it's free it won't actually charge you anything. After that, just check your library and then you can download each song and manually move it to itunes.
And hey thanks for the notification! Most of it isn't my kind of music, but I got the Dave Brubeck stuff.