You really should have a professional take a look. There is alot to take into consideration when it comes to sizing a pump for a sprinkler system.
Personally, I am a fan of Myers or Munro pumps, dependable and easily serviceable. Spendy but worth it. Brass impellers, multiple sizes.
I also build sprinkler pumps using 4″ submersible well pumps. The benefit is cost and ease of operation. No priming recquired. No risk of losing prime and burning up the pump. Smaller hp submersible will outperform higher hp centrifugal pump.
Most pump systems are run off of a pump start relay that is connected to the sprinkler controller. You will need live 220V to the lake.