Well, if you insist on pushups/pullups, I would start slow with the weight. If it were me, I would simply pick a total number of reps for each exercise as your target, and do as many sets as it takes to get that total.
Back in the Marines, one of my favorite things I used to do was to have a target of 50 pullups, and 100 pushups. I would alternate between the two.. One set of pullups, one set of pushups. In my mind, I liked to do 10 pullups, 20 pushups each set. I never had a weight vest though, which would've come in handy for sure! I used a DB between my legs.
As the weight increased, the reps decreased, meaning it took a lot more sets to reach my target.
I would start off with something managable. Add a little weight (10 lbs) and pick a target that you know you could hit. Start off with a prerequisite such as alternating between 'x' amount of pullups and 'x' amount of pushups.
As the weight increases, your muscles will adapt to the increasing demands you're putting on them and grow. Just be sure you're eating to grow as well!