Which partitions do I actually need?

I've got Windows 7 Home Premium 64bit, and I was wanting to install another OS, for various reasons. After reading about it online I found out that I should install it on another partition however no more that 4 can be created on a basic disk, but OS's can be installed on a dynamic disk. I've tried installing it on external devices, USB sticks, external HDD's, etc. but none worked. So I've come to the conclusion that I can either delete one of the existing partitions or forget about it. The attached image shows how the partions are layed out, along with names. I know some of them can be deleted, such as the C drive and Recovery, but HP tools and the other one, can they? I would appreciated any help. Thanks.

It's mac os x, which I know is compatible with my system. Also only 4 partitions can be created on a basic disk onto which OS's can be installed. No OS's can be installed on a dynamic disk, but more partitions can be created on it.

I've tried virtual box, but for whatever reason it doesn't run Mac OS X at any sort of usable speed, it takes like 10 mins to boot up. It probably doesn't like running 2 OS's simultaneously. What is actually stored in the HP_tools partition. Because I use the webcam software that came with my PC, and also it has some Cyberlink movie software which is quite good, so I want to keep those.

I do use the built in windows backup, but I can't back HP tools and system partitions up. But I can backup the program files and other files on the c drive.

So which partitions do I actually need to run Windows 7 properly. I don't want to delete the recovery partition because I'm not brilliant at keeping CDs, as proven by the fact that I can't fine the recovery discs I made when I first got the PC.