In terms of primary weapons, Snake for speedruns or Spur for a casual run. Super Missiles are the best for the bosses. Nemesis is a great weapon to have in the right situation as well, especially when you can have two with Curly. The rest of the weapons might have some use in more situational circumstances, but are overall too niche and underpowered compared to the ones I listed, I feel.
try to get as much levels for the super missiles in the beginning areas. Then you can use curly's nemesis for short range and the spur for long range. If you get to the heavy press boss spam as much super missiles as you possibly can and voila.
I'd say the Spur, Smissiles, and Nemesis are the best for this. When you get to the Heavy Press, wait for it's opening attack, switch to the Nemesis, look up, and mash as fast as you can. For Ballos, use the Spur. (If you didn't know) You can stand in ballos' eye after phase 1. Stand here, charge the Spur, and fire into both of his eyes at once.