Unfortunately, there aren't many cars that would meet all those requirements under Rs 13 lakh. You could increase your budget and get a more premium offering, or be prepared to sacrifice a few things and stick with your budget. 

Within your budget, your two best bets are the Nissan Magnite and Renault Kiger, which both offer exceptional value for money. They come with 1.0-litre turbo petrol engines and smooth CVT auto gearboxes, and if driven carefully, can deliver good fuel economy. Their touchscreens are decent but not great, and it's a similar story with their audio systems; neither gets a sunroof. 

The Hyundai Exter and Tata Punch facelifts are more affordable but not spacious enough for five, and get clunky AMT auto gearboxes. 

If you want to buy any of these SUVs, we suggest increasing your budget by ₹2-3 lakh. At a ₹10 lakh on-road budget, you will have to settle for the lower variants, which is a personal choice but does mean missing out on key features. 

Within a ₹10 lakh budget, a good option for you is the Hyundai Exter. It allows you to choose a fully loaded variant that comes with an 8-inch touchscreen, sunroof, cruise control, wireless phone charger, rearview camera, and other useful features. It gets a smooth and refined 1.2-litre, 4-cylinder engine that delivers power in a predictable and easy-to-manage manner. 

Since you are a new driver, opting for the AMT would be a sensible choice, as it adds to everyday driving comfort and convenience.

Amongst the cars you mentioned, you can consider the Tata Nexon or Kia Sonet. 

You can go with the Hyundai Exter AMT, it is a well-equipped car, drives well and has the smoothest AMTs in the segment. The 1.2-litre, 4-cylinder naturally aspirated petrol engine is smooth, refined and linearly delivers its power. 

For a first-time car owner, Hyundai's vast network of service centres and relatively pocket-friendly after-sales service will add to your ownership experience. 

The Maruti Suzuki Baleno or even its sister car, the Toyota Glanza, would be a good option to buy. The car is spacious with comfy seats, and it is fuel-efficient too, both the manual and the automatic version (AMT). 

In our standard test cycle, we got 13.80kpl and 17.50kpl in our city and highway cycles for the manual, whereas the automated manual transmission (AMT) achieved 11.86kpl and 17.21kpl.  

The Baleno sits below 4 meters in length and is compact enough for the city. However, if you would like something smaller, consider the Hyundai Exter. It won't be as efficient, in the manual we got 9kpl and 14kpl for city and highway runs, but this is still good. Also, you will also benefit from a slightly higher seating position and a lower price.    

Switching from E10 to E20 fuel reduces fuel efficiency, especially on pre-BS6 cars, so it's no surprise that you are refuelling more frequently and spending more at the pumps. It’s best to buy a new car, and for your budget, an ICE option is the best, as all ICE cars are now E20 compliant with engines designed to run on the higher ethanol blend. 

An EV at this price point will be a compromise both in terms of size and range. For Rs. 10 lakh, go for the Hyundai Exter, which is a well-equipped car that drives exceptionally well. Being a Hyundai car, it will feel familiar as well.

• Hatchback: Maruti Suzuki Swift
• Compact sedan: Honda Amaze, Maruti Suzuki Dzire
• Compact SUV/Crossover: Maruti Suzuki Fronx, Maruti Suzuki Brezza, Hyundai Exter

You can consider the Hyundai Exter AMT. It comes with one of the smoothest AMTs in the segment, offers a comfortable ride and has precise handling. The Exter feels stable and confident on the highway, while on the highway, it is easy to maneuver in city traffic. 

It is also well equipped, with a thoughtfully designed cabin that makes excellent use of the available space.