Help! Slow Battery Discharge

I have a 1973 Dart with a built 360 that has a holley blue fuel pump that i have had similar issues with the battery going dead. We discovered and corrected an issue with the brakes and rear brake lights that was causing a draw on the battery while the car was sitting. I still have an issue with the battery's power being drawn down while starting the car and it will go dead. Could the fuel pump be the issue and would switching to an Optima red top battery help? I only drive the car on weekends. I appreciate your help and suggestions.