You will be able to use almost any HDD which has the same connector as the old one. Looking at the specs, I believe you may have a SATA connector, so any SATA HDD or SSD should do. The only limitation I would put in place, is to not have a drive larger than 2TB, as older machnes can have problems seeing drives larger than this. The 240GB Kingston SSD should be fine, and probably help it be snappier than it was with an HDD.
The reason the other drive won't have booted via USB, is that you need special drivers to be able to do this built into an installation. It's unlikely the drive you used had USB boot time drivers installed, and it would fail half way through booting. Also, as coromonadalix intimated, the drivers installed on that drive for another laptop, may not have been the correct ones for the pavillion, so even if you install the drive inside, it may still bluescreen and/or not boot properly. Putting in a new drive, and doing a fresh install of windows, and any required drivers, would be the way to get it up and running as it should. Which drivers you need would depend on which version of windows you install, if you even choose to install Windows. There are other options out there too, I have an older laptop with linux mint installed.
TLDR -get the Kingson SSD, it should work fine. :-)