Western Digital, Samsung, and Seagate are the predominant brands. You can have bad luck with any of them, but I would lean toward the first two.
I'd get a size at least as big as your 640. There won't be much price difference if you go larger.
Some people here use Windows backup successfully, but others find it lacks flexibility and isn't intuitive.
Distinguish between the 2 forms of backup: imaging and file by file. The general problem with imaging is that it doesn't always work---you think you have a valid backup, but then can't restore it for whatever reason.
You should definitely do file by file for your personal data.
Optionally, you can use imaging to make an image of your entire C partition. That image file would include any personal data you might have on C, but I would still make a separate file by file backup of personal data.
You can store it all on the external. I'd just make a single partition on the external and use a folder structure to organize your backups, whatever they may be.
The primary alternative to Windows for imaging are Acronis and Macrium Reflect Free Edition. You can also get a free copy of Acronis is you have a Seagate or Western Digital hard drive.
There are a number of file by file backup applications: Synctoy from Microsoft, Karen's Replicator, Cobian, Second Copy, etc. Most people use a free application of some type.
You might consider making 2 partitions on your boot drive if you haven't already done so: C for Windows and D for personal data. You could then make an image of C alone or D alone or both. And also make file by file backups of D alone.