As a runner, the focus of the upper-body workout should be to gain muscular endurance. So, go with lighter weights and higher repetitions. 10lbs to 15lbs dumbbells are sufficient for this workout. You can also use light or medium resistance bands or resistance tubes instead of dumbbells.
The workout consists of a 7-exercise circuit. Do each exercise (10-15 reps) one right after the other without taking a break. Once you've completed all 7 exercises, take a 1- to 2-minute rest; then repeat the circuit a second time. If you're new to upper-body exercises, then begin with 10 repetitions. Each day add an additional rep until you get to 15 repetitions. Also, if upper-body exercise is new to you, begin with one cycle of the circuit for the first week. During Week 2, complete two cycles of the circuit. If you're advanced, try three cycles of the circuit.
It's fine to pair the upper-body circuit with the core workout on the same day. Try doing the core workout in the morning and the upper-body circuit in the evening. You can also rotate days. For example you could do the upper-body workout on M,W,F and do the core workout on T,TH,S. The great thing about circuit workouts is that they're quick. You'll have a strong core and upper body before you know it and you'll start to see the benefits in your long runs too!