Hyundai i20

Given your requirements, you should choose between the Maruti Suzuki Baleno and Hyundai i20. The Baleno comes with an efficient 1.2-litre naturally aspirated petrol engine that's mated to a 5-speed AMT automatic. It has a spacious cabin, and being a Maruti car, it will be reliable and affordable to maintain. The i20, meanwhile, also comes with a 1.2-litre naturally aspirated petrol engine, but that comes mated to a smoother CVT automatic gearbox. Do note, this Hyundai car can also be had with a punchy 120hp, 1.0-litre turbo-petrol engine mated to a 7-speed dual-clutch automatic in the i20 N Line. 

If you are open to buying an electric vehicle, the Tata Tiago EV is a good option for city use. It's got a smooth powertrain and is much more practical than the MG Comet you also considered. There's also the option of the Tata Punch EV, though it is slightly out of your budget. 

Among petrol automatic cars within your budget, the Hyundai i20 iVT and Citroen C3 AT have the smoothest automatic gearboxes. The Maruti Suzuki Swift AMT is also a good city car, though the AMT gearbox isn't as nice. 
 

There are plenty of options available under Rs 10 lakh and in different body styles. Since you were considering a small SUV like the Tata Punch, you could also consider the Hyundai Exter, which also comes with an AMT automatic gearbox, a smooth 1.2-litre engine, plenty of features, and it should be easier to live with too. Read our full comparison review between the Tata Punch and Hyundai Exter to get a more in-depth understanding. 

If you prefer a sedan, go for the Maruti Suzuki Dzire, which comes with a 1.2-litre petrol engine paired with an AMT auto gearbox, a comfy cabin and plenty of features. As for hatchbacks, the Hyundai i20 makes a good option as it comes with a smoother CVT automatic compared to the AMTs in the others.