Purchases being able to play without downloading onto computer
If I purchase something is there a way to play the music without having to download it onto my computer as it takes up alot of memory
Subscribe to iTunes match and the content can be streamed, just be aware that if you lose your Internet connection for any reason, you will be unable to play the content.
Realistically, you should always have a local copy of your content in the event that something goes wrong.
If the expectation is to sync content to an iOS device, the content must be local on the computer to sync.
iOS device cannot stream content from iTunes Match.