I am missing half of the 200 or so songs I bought. This is probably due to insufficient Icloud? Is there a way to get the songs back?

Click on this link and read how to 'Redownload music' --> Redownload music - Apple Support

- Learn how to redownload music that you purchased from the iTunes Store. On iOS devices, Mac, and PC.

Songs aren't stored in iCloud unless you have an Apple Music or Match subscription. If they are ones you bought from Apple then they will normally be available as redownloads and won't be counted against any kind of iCloud storage plan you have anyway.