First off, please note that I am completely aware that the Gomu Gomu No Mi was listed as a Paramecia Fruit in an SBS page. But, after some long thoughts about I have come to the conclusion that Luffy's Devil Fruit should actually be categorized as a Logia Fruit.
From what we have experienced, a Paramecia fruit gives you a superhuman ability and or alters attributes of your body like the number of "limbs" (also including Buggy and the Ball marine from the bridge) or the weight. These effects are used consciously and have to be activated by the user.
In contrast to that, a Logia Fruit transforms a body into a different kind of substance. This effect is permanent and the users don't have to make a conscious decision to use a fruits ability.
All of the traits we have seen with Logia fruits are present in Luffy as his body consists of rubber at all times and he doesn't have to make the decision to make a part of his rubber at a time or not.
My first suspicion to this came when Luffy got struck by one of Eneru's lightning attacks. Luffy didn't know what was coming to him and yet he came out unharmed. My thoughts came more to light when I recently reread the Enies Lobby arc and Lucci's explanation of Gear 2 in it and Luffy's arteries and heart valves and muscles consisting of Rubber. Luffys bones being rubber as well with Gear 3 only strengthens this argument.
That Luffy's fruit is always active can also be observed by him surviving Lucci's Higan to the throat largely unharmed. Or Luffy not being able to will himself not being Rubber when Usopp tried to pull him out of the concrete in Arlong Park.
The only counterargument that I can think off is that so far we have only seen Logia fruits of "elements" that are not a solid.
To counter that point I would like to ask you if you would categorize the hypothetical fruits that give you the power of the classical japanese elements of wood and metal as Logia or Paramecia fruits?