Thank you very much for the detailed and helpful reply, Steve. I should be good with the Time Machine automated backups I've been doing for years on an external USB HDD. The whole unit isn't bootable but I think the partition holding the BU is. I had the idea that a fresh install should be able to extract from a TM backup all the information needed to configure the programs when needed after the OS is installed, but probably I have a wrong idea of how it works.
I swapped the original 500GB HDD with a 250GB SSD, on that intervention I removed the optical drive and added a HDD 1TB unit, which is not the backup one. I also added RAM so the MBP has 8GB now. I did this like four or five years ago. However I didn't make a clean install, I took everything needed from Time Machine. I once tried a clean install from a SD memory card, when Mountain Lion was released, but I didn't get the thing to work, that's why I'm a bit hesitant to try the procedure.
Since I'm absolutely OSX command line incapable I'm more pronte to try Disk Maker to create the bootable installer on a USB thumbdrive. As I'm writing this the HS installer is almost downloaded. Just one question, since I guess the install pack has the basic OS, is it more recommendable to apply all the updates before installing the apps? I'll check here for further recommendations before the erasing and installing.