Generally speaking, big backups tend to be written on media that are sequentially accessed. That being so, you won't want to use this complete backup for restoring significant numbers of files; it's got too many files on it that you don't want. It's better to create small backups of individual segments that you know you're going to restore in their entirety. I'll list a bunch of examples later.
Why then should you start with a full backup? Two basic reasons: first, in the event of a catastrophic failure installing the new system, you'll have a way to get back to the starting point with minimum pain. Second, no matter how carefully you prepare for the new installation, there is a very large chance that one or two important files will be overlooked. In that case the clumsiness of restoring those one or two files from the full backup set will be preferable to the inconvenience of doing without them.
To save time and space, if you've still got the distribution medium for your old linux version, you might want to back up only those files the mtime or ctime of which is more recent than the date of the original installation.