Taking a step back, are you doing any kind of backup, or is everything you digitally own on your macbook? The absolute simplest thing to do would be to get an external drive and move some of the stuff you don't need with you at all times over to that.
If you want to add internal storage and would rather not disturb your existing hard drive, replacing the DVD drive with a second hard drive would be the most straightforward solution. But that process is more involved than swapping the hard drive, so that might not be for you if you are already hesitant about opening your mac. You would need to buy any 2.5" drive along with the caddy linked below.
hard drive caddy at OWC ---
dvd drive replacement at iFixit
_______________________________
If you want to go ahead with replacing your existing drive, the best option would be an SSD which would speed up your machine considerably. But those are expensive in 1TB sizes. ---
Crucial 1TB SSD at Amazon
For a typical hard drive replacement, if you don't care about speed as much, I would just get a 2TB drive which should last you quite awhile. ---
Samsung 2TB at Amazon.
For a 1TB I would get this
Seagate hybrid, which has 8GB of flash memory, so it works somewhat like an SSD - it will learn and store your most-used files on the flash memory portion. But any 2.5" 1TB drive should work.
_______________________________
You can get any cheap
2.5" USB enclosure to use for cloning -
this tool-free one looks pretty simple and slick. Put the new drive in the enclosure, clone over your existing drive, then
do the swap. Note this will take awhile as you only have USB 2.0 ports on your macbook.
Carbon Copy Cloner is what most people seem to like for this.
The best solution for your particular machine would be an enclosure that includes Firewire. These are a little harder to find, but here is a very cheap
Acomdata on Amazon. For that one you will also need a
Firewire 400 to 800 cable to attach from the drive to your Macbook. This will be much faster than USB 2, and also allows you to boot from it, so you can verify that the clone worked before you open up your macbook to swap the drives.