What types?
The more powerful the weapon (power being determined in a fairly arbitrary way at times, but that's the intent) the higher the level of licence you need.
I've probably got the two highest level licences a civilian can get without too much difficulty - I hold a Category D licence and a general category handgun licence.
Category D allows me to own most semi-automatic rifles and shotguns. My handgun licence allows me to own a non-automatic handgun that is .38 calibre or less and has a barrel length of over four inches.
(A category C licence allows small magazine semi-automatic weapons, a category A/B allows single shot longarms - hunting weapons like .22s and shotguns for duck hunting. A Category E licence allows for machine guns and similar - technically it's supposed to be possible to get such a licence as a civilian, but I've never heard of anybody doing it. There are also licences to allow people to own handguns outside the 'general category' but again they are unusual).