Welcome to the board there is a lot of people here to help... Yes it will start better with the electric start more constant revolutions than the pull starter. Good luck with the ebay thing but i just saw a bunch of 125 parts on there.
I couldn't get my 110 started and had to pull start it for about 100 yards or so before it worked out its issues. Now it starts on 3rd pull. The carb sounds like it may need rebuilt this will help with starting issues also. good luck and have fun!!
1982 Honda 185 My work horse
1985 Honda 125 kids love it
1984 Honda 200S My main ride