Any training can cause injury
I am wary of bodyweight training just as much as I am wary of barbell training. Both have their risks, including tendonitis, shoulder trouble, and back problems.
Overtraining is an issue under any overzealous progression. What you are looking for is not marked by any particular tool, but by cautious progression.
Workout progression to prevent re-injury
If I'm cautious with an existing injury or overuse situation, what works for me is a slower and more cautious progression: for instance, when working around an inflamed shoulder I started with three sets of five dips. I was capable of doing many more, but I took it super slow. The next workouts looked like this:
- Three sets of five again
- Three sets of six
- Three sets of six
- Four sets of six, since I wanted more volume but felt that my form started to deteriorate ever so slightly towards the end of a set
- Four sets of six
- Four sets of seven
- Three sets of eight
- Three sets of eight for several workouts until it felt easy and I didn't need much rest between sets
- Three sets of ten
- ...more gradual progression until I was hitting three sets of twenty or multiple sets with added weight
I think this approach works well for coming back from an injury and taking it easy on potential injuries.
A similar approach works for barbells, too. (Again, there's nothing inherent about barbells that makes them more prone to causing injury than a set of gymnastic rings.) What was recommended to me was:
- Back squat, warm up then three sets of 20 reps at a low weight, increasing weight only when the current weight is easy. When the weight gets to 135, switch to 3x5 and add 5 pounds once a week or even less often.
- Romanian deadlift, warm up then one set of 10, increasing the weight only when you have perfect form and the weight is boringly easy. Switch to regular deadlifts for sets of 5 when the weight is heavy, and consider snatch-grip deadlifts to emphasize mobility and the upper back.
This is one way to take it slow and easy with barbells. The slower rate of adding weight and the higher-rep starting period both allow more time for the tendons to grow in line with the muscles.
It sounds like you're concerned first and foremost with a healthy, balanced body rather than looking big or impressing people with numbers. For those purposes, I'd focus on a variety of exercises and picking those exercises based on movement patterns and balanced combinations of movements.
- Exercise variety: don't strive to be good at pull-ups...strive to be good at pull-ups, chin-ups, muscle-ups, windshield wipers, barbell rows, and dumbbell rows. Not all at one time and not quickly, but switching cautiously among similar exercises helps ensure we don't get too adapted to one particular challenge.
- Movement patterns: classify exercises in groups such as pulling, pushing, squatting, hinging (deadlifting), carrying things, locomoting (walking, dragging things, running, swimming, crawling, brachiating...). Keep in mind the distinction between fast and slow movements; deadlifting and power cleaning are intertwined and mutually beneficial just like sprinting and going for a walk with a friend.
- Combining movements: for each push you pick a pull, and for each squat you pick a deadlift, and if you've been doing an overhead push for several months maybe you switch to downward pushes (dips) for a while.
Research for approaches like this
If you want to figure out a similar approach to this, it may help to see where I got these ideas. The movement patterns is an amalgam of Dan John (see his book with Pavel) and Ido Portal (browse his site and gymnasticbodies.com's forums for his posts). The rest was cobbled together from guesswork, programs recommended to me by friends, Coach Sommer's forum posts and articles referencing his Building the Gymnastic Body project, Rippetoe & Kilgore's Starting Strength (which has a lot of philosophy and productive discussion about organizing training) and Practical Programming (which goes into the science of strength training), as well as Tom Kurz's heavily-referenced elite-sports tome Science of Sports Training.