I have lost my manual to my Sears Eager-1 5.0 push mower. I drained the oil (don't ask why I did this first). What kind of oil do I put back in it? Regular 10w-30? Thank you for help.

I have an Sears Eager-1 5.0 push lawnmower. Alright, I changed the oil and put in SAE 30, a new spark plug, and a new air filter. I can see no bubbles in the gas tank indicating water (I ran it out before the Winter and put new in in this Spring). However, it still will not start. I got GumOut, took the air filter off and sprayed the Gumout into the carburetor. It started and quickly died out. I did this about ten times. This told me that continuing gas was not making it. So, under the primer pump on the carburator is *something* I took it off and it had a round ring looking thing attached to a little plunger with a pin. When the plunger was pulled out the gas came. I put it back on and didn't put it back on tight enough at first, but gas was coming in the carburetor - pull and it started, but because it is not continuing to get gas it does the same as the Gumout treatment - it dies a few seconds later. I screwed the piece back in further so the gas didn't just spill into the carburetor and no start. What is this called here? What do I replace? Thank you for taking the time to read this. I know it was long.