Should be NO problem.
(1) Most newer laptopds do NOT come with the "recovery" disk. If you check the manual you will probablly see - "Make Your OWN. usally 3 -> 5 DVDs. make sure you do this first.
(2) Pop out the original HDD. Usally one or two screws holding the cover on. and probably 4 screws that hold the HDD in place. Hopefully, HP included the "holder" for a 2nd HDD, since you have two bays. (My Samsung FR711 came with single drive but two holders.
(3) Put the new drive into the same drive bay. Try out your NEWLY completed recovery DVDs. Boot to new HDD and check that all partitions have been install. probably will see up to 3 (use Windows Disk management to view drive as some partitions may be hidden from My computer).
Some tips:
A) Do NOT erase the orginial OS for at least a Month.
B) Your Old drive probaby has a "C"-drive (partition), a recovery Partition and a Sytem partition. These last two may be small and hidden from MyComputer. What I would do is "shrink the C-drive partion down to about 100 -> 110 Gigs and make a D-drive out of the now Unpartitioned space. Use this space for Your overflow/ or any files you want to place on the old drive. Then, at least for 1 -> 3 Months do NOT delete the orginial OS.
On the newly "cloned" HDD. Same-Same, shrink c drive down about 100 Gigs. This can be down from computer management. Create a D drive for all You data from the "left over space. Get ride of the Bloat ware that will be preload, install all your programs Check out for a week.
Every thing OK, then use Windows Bck-up to create an image of the C-drive. Can either place on a HDD (my preference a external HDD), or on DVDs. USE this to re-insall in future an not the "restore" disk that you made. This way all the programs you installed would be included and you would Not have to go thru and delete all the bloatware.
Since you have two HDD bays, a better option (from a Performance) stand point would be to buy either a 128 gig curcial M4, or Samsung 830 SSD.. SSDs run circles around HDD while althe time laughing!!. The HDD is probably close to a $100, the M4 can KNOW be found on sale for around $120->$140. Place your OS and programs on the SSD and all your data on a HDD in Bay 2. This is what I did with My Samsung RF-711 Laptop.
ADDED:
Kits, for laptop, generally means that it comes with software to clone HDD to the New drive. or
If for a desktop the kit will include a a 2 1/2" -> 3 1/2 in adaptor.
OEM is just a bare drive (and normally the mounting screws to mount drive to either a adaptor or a caddy).
For laptop and Mounting in 2nd Bay, you do not need any extra cables, in most cases the drive will Plug directly into a connector on the MB - No Cable required. No New screws should NOT be needed providing the Laptop comes with the caddy to mount the HDD (or SSD) in The screws for mounting the caddy (once HDD is pushed int connector) will either be inplace and you will need to remove, or in a small ziplock baggy.