Unless your application is
portable (keeps settings in a file, doesn't write to registry, doesn't need system-specific libraries, runs on any other system with the same OS without reconfiguration), it might not work again after a reformat. Backing it up doesn't guarantee it'll work.
Consider replacing the apps you use with
portable versions, and reformatting should be much less of a pain.
Also, reformatting should not be used as a regular system cleanup measure; it would be best if you can figure out what's causing the issue. I would be curious about why your internet connection gets laggy every few months... are you sure it's your connection being laggy, or is it your system?
If you insist on getting a single drive just for your OS, though, I'd go with a small SSD. They're fairly cheap at low capacities and are way better performance wise.
LMAO... he's going for the cheapest drive he can find, and you're recommending an SSD?

The ones that are cheaper than hard drives are not faster than hard drives, sadly... the cheapest small SSD I would recommend would be something like the
OCZ 30GB Vertex (or an equivalent drive using Indilinx firmware).
For a small budget I'd go for a decent-sized WD Black, and keep documents (large video files, images), as well as the pagefile and temp folder, on the old hard disk. It might bump up the budget a bit since the smallest Black is 500GB, but if that's still too pricey, the Blues are decent performers for the price as well.
You don't need a new hard drive. Set up your page file on a separate partition, defrag every couple of weeks, and don't download torrents to the same partition on which your OS and applications are installed.
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