You could partition any external drive so one partition is for Time Machine backups of your MBP and the other partition is for iTunes and media. Disk Utility in the Utilities folder can partition anything to your heart's desire.
As for accessing your media via the Internet, you have several choices. One is to use an app like Orb (many versions, but you would want the free Orb Caster on the machine with the media and the $9.99 iOS app), which will stream music/video over the web to any device you want. The only drawback you need to have a computer at home that the media can be accessed through, i.e., your MBP, which is fine if you only want to access the media on an iOS device while out.
Another choice is to buy an optical hard drive caddy to put in your optical drive slot and just put a large, 2nd hard drive there, right in the MBP. It's easy to do and the caddy's only cost $15-20 U.S. for most brands (plus the cost of the hard drive). If you put a 1TB hd in as a 2nd drive you could partition that for both Time Machine and your media and not need an external drive (although having an external drive for backups is a good idea when you have a laptop in case it's stolen, lost, or significantly damaged and you can't get to what you need).
The last option is to use either iTunes Match, Google Play, or Amazon Cloud to upload your iTunes music to the web. It won't do any video, and none of those 3 do that great of a job actually matching your songs and getting them correct on the cloud. iTunes Match and Amazon Cloud are paid services. Google Play is free, but there is no app for iOS devices or Macs, you access your music through a browser.
Orb is fantastic, and will stream music and videos, and I believe, can also find files, but don't quote me on that since it's been over a year since I used it (haven't had a need and it was completely free when I first started using it, now they have various free and paid versions depending on where you want to stream to). But as I said, Orb needs the media to be connected to a computer back at home, because Orb will be running on the computer at home and the computer or iOS device outside the house.