A:
An ATA drive may be replaced with a SATA drive under most conditions. The procedure is simple if you know what you're doing: open the PC, unplug (and mark!) the wires from the old drive, plug them into the new drive, and off you go. The only catch: if you're replacing the C: drive you will have to reinstall your operating system.
Your laptop, an HP2000-2c29WM, is a newer model. It already has a SATA drive; it's not a parallel ATA drive. If you check your specs you'll see the drive is called a "serial ATA" device. That is a SATA drive. The drive you wrote about is the installed drive. Unless you are having problems with it, I suggest you stick with it.
Problems can include either "it doesn't work" or "it's full." I'll tackle the second one first: purchase a second, external drive. A 1Tb external drive is inexpensive and plugs into a USB port. No technical expertise is needed; consider it a giant thumb drive. Move your files there to free up space on your main drive.
If the drive is dead (won't boot, or you can't log in), you must replace it. Below find some suggestions.
To restate, I don't recommend replacing the drive unless you have to.
Your current drive is SATA, 500 Gb, and 5400 RPM. SATA drives run from 5,400 up to 10,000 RPM. A word of caution: the faster the spin rate the hotter it runs and the more electricity it uses, which is not good for the drive or the environment. Stick to 7200 RPM and you'll be fine unless you absolutely require the fastest speeds.
If you are going to replace the drive despite your not needing to, here are my recommendations. I added three "recommended products" for comparison purposes only; I'm not trying to sell anything in particular.
Brand: Western Digital or Seagate
Type: SATA SSD (solid state drive, if you can afford it) or SATA spindle drive at 7,200 RPM.
Capacity: 500Gb or larger, up to 3Tb.
Form factor: laptop drive or external box.
Usage: external should be the choice; if you replace the internal drive you'll have to reinstall Windows, and that will probably involve paying someone to install the drive and install the OS. If you go external just buy the drive; they're plug-and-play.
I can't stress this enough: unless you are having problems with your drive, don't replace it; it's not worth the hassle. I build my own PCs and I wouldn't do it; if you're not technically inclined, the simple solution is the best.