I suggest, instead of fighting the two dogs now, you skip all fights until the arcade. When you kill starman junior you'll reach level 2.
You're gonna be forced into fighting two battles in the arcade:
Pogo Punk - 35 hp (two smash attacks kills him.) he gives 15 exp. That will level you up to level 3.
Yes Man Jr. - 33 hp (two smash attacks kills him, also.) he gives 13 exp. That will make you level 4, with 65 exp. to the next level.
You can choose to run from those fights and avoid the exp. but since you plan on leveling that seems like the fastest method. Unless you spend time leveling up, you're fighting Franky in level 4.
When I tried those fights just now I was using the craked bat. If you buy the better bat it's possible that you could take them out in a single hit. I don't know for sure.
Just thought I'd suggest that method since it seems faster than what you chose to do and it's gonna get you the same level, unless, of course, you plan on leveling up before Franky, which I do not suggest.
EDIT: Also, you should abuse death as a shortcut whenever possible, since, when you die the game takes you to the last save location with all progress still completed. The only downside to that is you lose half your money on hand... but that shouldn't be a problem for you at all.
EDIT EDIT: (This is the last edit for this post, I swear. I'm absent minded lol.) I suggest you use this
http://starmen.net/mother2/miscinfo/battleenemy_guide.txt to help you for enemies and boss battles. Has everything you need to know on the monsters. Hp, exp. and etc.
