If you want to go for Honda Amaze, the diesel engine is the most powerful in the segment. It produces the maximum power (100 bhp) when compared to it's rivals. The pick up of the car is also very good and the acceleration is also quite amazing.
It does not feel sluggish when starting out as there is no lag in the power transmitted to the wheels. The gear changes are also very crisp. The ride quality of the Honda Amaze is also very nice and firm. Even when you are driving at high speeds like 110 kms/hr the car is in Eco mode i.e it still is giving you a very good mileage.
The only possible issue is the engine noise that filters into the cabin when you are driving. The petrol engine is also quite nice but not as powerful as the diesel. The initial acceleration on the petrol is better than the diesel but the overall performance in the diesel is much better. If a little engine noise is not an issue for you, we would suggest to go for the Diesel as it is a better engine for the driving pleasure.
The engine noise is coming in the cabin because of poor cabin insulation and it depends on various things like gaps between panels and doors, material quality, etc. You need to get major changes in the interior for better insulation and we won't recommend that.
You should go for the fourth servicing despite the fact that you have not driven your car much. It is important that you go for regular servicing. Whether you want to go for wheel balancing should depend on if your car is bobbing while driving or it is not going in straight line.
The choice of the variant between diesel and petrol would depend on what would be your monthly run. If your monthly run is more than 1500 kms, you should go for the diesel variant else you should go for the petrol variant.