Your pulse rate doesn't always reflect fitness, so on its own it's not a reliable indicator.
Doctors take a statistical view, so the 'standard' position would be that anything under 70 is good; under 60 very good.
Unfortunately, a low pulse rate can indicate problems, too. If you don't have other indications of fitness (such as a long-term running history, good lung capacity, high strength and appetite, small waist for height), you might benefit from being examined.
(The only significant early symptom of Hypertrophic Cardiomyopathy, which causes sudden heart failure, is a low pulse rate. There are plenty of people walking around thinking they're pretty damn fit because they have a low resting heart rate, who are at risk of dying without warning. The cardiac overgrowth involved CAN actually give better aerobic performance, so a lot of the victims have been 'naturally gifted' sports participants. However, unless they are ACTUALLY an olympic athlete (kidding themselves that they're training at the same level is no protection), a heart rate under 40 is a danger sign, not a cause for congratulations. If anybody out there knows somebody like this, please get them to get checked out ! )
Higher resting rates than this can still be a symptom, but statistically, having survived to 68, HCM is not very likely to be a problem for you.
Age-related changes to bodyfat are also unreliable; overall bodyfat tends to increase, although the amount stored in the skin will often decrease. (again, it's the 'intra-abdominal' fat, or spreading waistline, that's most harmful).
Try
www.acsm.org
or
www.fitness.com