Would the present 3*10 sets work best with Sandbags, I plan on progressing to 3*15.
Yeah, I'd think it would work better, but it's always been my experience that sandbags don't work best in a sets x reps context. In my experience, the best use of sandbags has been with a max reps in a certain amount of time type routine. One I used to do was the 50/20 routine. I did it with sandbag shouldering where I would shoulder the sandbag, drop it, shoulder it to the opposite side and repeat for as many times as possible in 20 minutes. If I got 50 reps total (25 per side) I would add weight (5%) to the sandbag next time. The routine could just as easily be done with throws, cleans, snatches, etc. Other great exercises with a sandbag are carries, carrying them for distance, carry them up stairs, do walking lunges with them carried on one shoulder, across your shoulders (behind your head), bear hug style or overhead.
I'm in a situation similar to yours, no gym, just a pullup//dip station at home some plates, and a kettlebell. I would recommend something similar to my routine:
Monday
Dips - 5, 4, 2x3 @ 0, 25, 50, 75; 2x5 @ 50
Pistols - 5, 4, 4x3 @ 0, 10, 25, 35, 40, 40
Pull-Ups - 4x8 @ 30
Finisher: 50/20 drill with sandbag shouldering
Wednesday
Pistols - 5x5 @ bodyweight
Pullups - 5x 10 @ bodyweight
Density training with sandbag clean + 2 presses
Finisher - overhead carry or lunge for while
Friday
Dips 5 @ 25; 4 @ 50; 3 x 3 @ 70
Pistols 5, 4, 3, 2, 3 @ 0, 10, 25, 35, 45, 50
Pull-Ups - 4x8 @ 30
Finisher: 50/20 drill with sandbag shouldering or some other sandbag exercise (snatches maybe I don't know)
To add weight to pistols I recommend a cheap barbell held in front squat position (arms folded style). if you don't have a bar try holding a plate behind your head. if you don't have any plates, then well... I dunno, go fucking get some. If you can't do pistols with weight, do more reps. If you can't do pistols, do lunges.
Cookie cutter routine based on no knowledge of your previous training experience, your current level of fitness, your goals, your abilities or health. Your mileage may vary.