iTunes on New Macbook Un-Downloaded Songs/ Playlists

I have a new MacBook Pro and connected my iTunes account to it. But all of my playlists and a lot of my songs that I had on my old computer were deleted and all the songs that are there are un-downloaded on my new computer. The iCloud Download symbol is next to every single song, but not all of my songs that I had on the other computer are there. And all of my playlists are gone. Is there any way to get the songs and playlists downloaded onto my new computer like I have on my old computer? (Preferably without taking up a lot of space on my new laptop if possible)

Thank you in advance!