Given your priorities, we would recommend you look at the Mahindra XUV 3XO in compact SUVs. It's got a tough build, strong engines and scored well in terms of cabin space. Alternatively, you could look at the turbo versions of the Nissan Magnite and Renault Kiger. The two models are underrated and actually deliver great value for money. 

Among sedans, if you don't mind the absence of many tech and comfort features, the entry-level Skoda Slavia and Volkswagen Virtus are worth considering. Their strong turbo-petrol engines and tough build are highlights. If you want more features, there's the Maruti Suzuki Dzire, but you'll have to compromise on power and performance. 

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. 

The Nissan Magnite and Renault Kiger share their turbo-petrol CVT (automatic), which is a smooth yet powerful powertrain option. 

Both cars have been refreshed recently with quite a few upmarket touches. Between the two, the Magnite looks a bit more SUVish and has slightly better cabin ergonomics. 

If you have a Citroen touchpoint nearby, you must check out the C3 Turbo AT. It is a much better car at a more affordable price tag.

Given your requirements, the Nissan Magnite and Renault Kiger are worth a look. There's plenty of space for rear seat passengers, and there is enough room for three passengers to sit in the back in reasonable comfort. 

You could also consider the superbly packaged Renault Triber. It's three rows of seats give lots of flexibility in seating, and the option to slide the middle row also means you can open up lots of legroom by moving the seat to its rearward position. 

There are a plethora of automatic petrol cars available within your budget. Given your monthly travel is just 200-300km, we will give less weightage to fuel economy and more weightage to driving comfort. As we don't know other preferences, here's a shortlist of the best options by body style -  

Hatchback - Hyundai i20 IVT Asta (O), Citroen C3 X Shine AT
Compact sedan - Honda Amaze CVT ZX
Compact SUV - Nissan Magnite Turbo CVT, Renault Kiger Turbo CVT Emotion

You're right, the Renault Kiger is a modern car which is decently equipped, but its resale value isn't as strong as some other options in this segment. The Kia Sonet feels more polished overall, and it will get you more features too. 

Yes, the iMT is convenient, but try getting a proper automatic instead, which will be a far more convenient and smoother option. If you want something a bit more modern, the Hyundai Venue is also an option you must consider. The Mahindra XUV3XO is also a compact SUV you may consider.