I would generally say that OSX upgrades are best applied fairly quickly. Maybe not the first week or so but soon enough. We have Macs of various ages and all have been done without real issue.
One of the main elements to enable an OS upgrade is enough space on the hard disc to download a New OS and then migrate the entire content. This means that it is best to remove old and unused stuff to an external point (Apple Airport Express is a wifi access point with a hard disc in it which can automate the entire backup process, not cheap but sooooo simple) Make certain you clear as much space as possible prior to doing it. Minimum would be 10Gb but I would recommend doubling this for speed.
Always do a backup beforehand. A simple portable hard disc (ebuyer 2Tb portable USB3 hard disc for £70) will do it. Look for Time Machine which is the built in backup and restore app which is great. An Apple TimeMachne 2Tb requires more money and installation but is great. Get someone to help you if you go the timemachine route. If other people have Macs in your home it can back these up as well.
