But you COULD choose your character in the original arcade game...
And you can.
As soon as you put coins in (default = "5" on your keyboard), the screen says "Press the Jump Button to start the game." That would be Button 2, for whichever character you want to play as. Again back to default keyboard controls, that would be "ALT" for George, "S" for Lizzie, or "RIGHT SHIFT" for Ralph.
If your controller works in MAME, and you want to play as Ralph, then re-define the buttons/sticks on your controller to match the Player 3 controls for this game. Click "TAB" to bring up the Config Menu, then select "Input (This Machine)."
The default controls for Player 3 are "I, K, J, L" for U/D/L/R, plus RIGHT CTRL and RIGHT SHIFT for the two buttons.
To redefine your controls, starting with "UP,"... highlight P3 Up in the menu, click ENTER on your keyboard, then click Up on the D-Pad or Stick you wish to use on your controller. Repeat for D/L/R and both buttons. Then you are good to go.
Suggest you go here and read:http://easyemu.mameworld.info/mameguide/Getting_Started.html
MAME is not like the game for your iPhone or XBox that starts out by teaching you how to use the game... it requires actually reading the user manual and some tinkering to get things to your liking.