Robot is a great character to start out with for its near limitless supply of ammo. This allows the player to stock up on weapons with scarce ammo (Triple Machine Gun, Laser Minigun), making killing hordes of enemies that much easier. With Robot's passive ability 'Better Tech' it will also find stronger weapons sooner making this character arguably the strongest in the early stages of the game (weapon wise).
Throne Butt - choosing Throne Butt is always a welcome addition as it will double the amount of consumables Robot receives.
Second Stomach - eating guns will heal you for double the amount.
Back Muscle - Robot's ability creates health and ammo which means sometimes you will reach the max ammo capacity. Back muscle will allow you to carry a greater supply and will ensure you rarely run out of ammo.
Open Mind - Robot's ability to eat spare weapons means that this mutation's random effects will always be useful, and it is a guaranteed extra resource on every level.
Heavy Heart - increases the chance for enemies to drop weapons which is always useful when playing Robot.
The Crown of Guns is a good pick for the character, as it gives Robot more "food" to eat and the nutrition gained from eating them negates the drawback of ammo not dropping.