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What should I start with to gain upper body strength

I'm trying to join the Canadian military, and need to pass the FORCE fitness test. I have never really kept up on my fitness, and for the test, I need to be able to do

  • Sandbag Lift: 30 consecutive lifts of a 20 kilogram sandbag above a height of 1 metre, alternating between left and right sandbags separated by 1.25 metres. Standard: 3 minutes 30 seconds.

  • Intermittent Loaded Shuttles: Using the 20 metre lines, complete ten 20 metre shuttles alternating between a loaded shuttle with a 20 kilogram sand bag and unloaded shuttles, for a total of 400 metres. Standard: 5 minutes 21 seconds.

  • 20-Metre Rushes: Starting from prone, complete two 20 metre shuttle sprints dropping to a prone position every 10 metres, for a total of 80 metres. Standard: 51 seconds.

  • Sandbag Drag: Carry one 20 kilogram sandbag and pull four on the floor over 20 metres without stopping. Standard: Complete without stopping

What would the best exercises to start with to be able to work out for this? I'm training for it at home I'm not going to get a gym membership because I will be getting one through school when it starts up. At home I have a barbell, and a dumbbell with the equivalent of 135 pounds of plates. (I have so many because I bought them both used, and they both came with their own sets of plates.)