>2 weeks off
That's retarded unless you're actually injured. Yeah, do a deload week every couple of months, but don't go "off" completely, just go lighter and less volume. *When* you deload is up to you, every 6, 12 weeks, when you feel like it,.. doesn't really matter.
>different specific programs
Why not do a bit of everything? Every one is limited in its own way, there's no advantage to split it up like that.
You don't have to do the same thing forever, but you should have some of each all the time.
Barbell Lifts should be the basis.
Bodyweight stuff you can do for a lot of volume (like, 100 pushups every day, 100 pullups every day, etc)
I don't know much about Kettlebells, but I don't see why you shouldn't just do a couple of KB exercises every workout, in addition to BB exercises (and DBs, machines if you need to)
It also depends on how often you want to train and what you have access to outside the gym.
The best starting point imo is a 4 day Barbell routine where you focus on one of the four Squat/Bench/Deadlift/OHP each day. And keep this basis for pretty much ever.
In the short term (daily-weekly), only change the weight. In the mid term, change sets and reps (weekly-monthly). In the long term, change the variation (6mo-year).
As I said for bodyweight stuff, volume volume volume. At least for the basics like pushups, pullups, dips. 100-200 reps each per day should be your target. How you get there is up to you. Between the barbell sets, sets of 10, sets to failure, whatever. If you want to do more technical stuff like muscle ups or handstands or whatever, I don't know too much about that, you'll have to look up routines and see how they fit your schedule.
Same for Kettlebells, I don't know anything about potential exercises and how they're programmed, so you gotta look that up.