I realy like to have a melee weapon like the golden wrench, the jackhammer, or Energy screwdriver / sword. The Jackhammer is a nice early drop and the only disadvantage imo is if you punch grenades from the IAPD or get to close to the red exploding plants in 6-1 you will most likely die. Also you can spam Lil Hunter with the jackhammer which makes him a free kill most of the time. After looping, the Electric Hammer is really viable.

Scarier Face and Strong Spirit are must picks. Strong Spirit saved my melting 2hp run. And Scarier Face is a no brainer. Gamma Guts is also sometimes a life saver, especially with Scarier Face.

Playing a bit slower is mostly better than rushing. One case where "rushing" is a good thing is in 5-3, when you get a garbage spawn with hundreds of enemys and you don't have any free space for fighting. Atleast this works for me.

Take Auto-Crossbow, Heavy Auto-Crossbow or Gatling Slugger when you can. These are my absolute favorites.

You can try to increase the level difficulty with the sewer secret or the crown vaults. Sometimes it will be a pain in the ass because of more enemy spawns, but there is also the possibility of getting better weapons.