Well, from what I know of computers I would say that when you do a full Linux install, it gives you the option to partition your drives. You can leave the C, D (odd that its D because thats usually reserved for CDs/DVDs), and E drive intact and create a new partition, or you can delete and merge the ones you want.
I would personally back up all your data to an external drive and completely wipe the computer if you are going for a full Linux computer. That way its all Linux and no hints of Windows (ie the Recovery Drives) will be left for any reason.
But, if you want to have a little bit of windows hanging around you can delete the C (which is the main windows obviously) and probably the E (Not really sure what is all in HP but since D is the recovery, I dont think its needed for anything special. Just extra crap that HP wants you to have) and leave the D drive there as I assume its only like 10GB usually for recovery. Then you delete/format the others and install linux onto the new fresh C spot and make it one large partition to take up the whole space.
In the end you will be left with C which is linux and E which is Windows Recovery.
That is my knowledge on the subject and I will be soon to follow in these footsteps because my Windows is starting to crash again. O.o Hope I helped some