Hero MotoCorp Xpulse 210

Considering your use case, we would advise choosing between the TVS Apache RTX 300 and the Hero Xpulse 210. The RTX is an adventure bike, which will make it great on the road, while the Xpulse is a dualsport, which will be more capable during serious off-roading. 

If you want a more road-biased machine, then the Honda CB350 H'ness (or either of its siblings), the Royal Enfield Classic / Bullet 350 and the TVS Ronin would make for a good option. 

Take a test ride of these machines to help decide which one is best for you. 

Both the Honda H'ness CB350 and the Royal Enfield Hunter 350 are great step-up options from your current Honda Shine 125 and will be able to handle bad roads reasonably well. 

However, if you want something that can tackle bad roads without breaking a sweat, the Hero Xpulse 210 is our recommendation. 

Since you are a beginner, we'd suggest that you start with something a little less powerful and easier to manage. As you've mentioned that you have an interest in mild off-road riding, the Hero Xpulse 210 would be a great place to start. It is a fun bike to ride, very comfortable in the city, and it will be a good motorcycle for you to hone your off-road skills on. Once you've gained some confidence, you can look at bigger ADV motorcycles. But if your heart is set on one of the above two bikes that you mentioned, we'd recommend you try out the Apache RTX 300. 

Adventure bikes generally have a tall seat and could be a challenge for you to manage with your height. With that in mind, we suggest that you start with a smaller, lighter ADV bike like the Hero Xpulse 200 or Xpulse 210. We would also urge you to attend an off-road riding academy, where you can learn techniques that will help you manage better on a bike with a tall seat 

The new Hero Xpulse 210 is a good choice as it makes for a very comfortable city commuter as well. You might find the seat height a little tall, so we'd suggest that you take a test ride before making a decision. If that's the case, you could consider other motorcycles like the TVS Apache RTR 160 or 200 or the new Yamaha XSR 155 as good upgrades

You can definitely learn on a Triumph Scrambler 400 XC, as it's a very forgiving 400cc 40hp machine; however, we would steer you toward the Hero Xpulse 210 instead. 

Considering you're also going to do some off-roading and you're simultaneously also going to be learning to ride a motorcycle, the Xpulse is a more forgiving machine than the Scrambler 400 and will be a better fit for city usage as well. 

Since you've come from a Hero motorcycle, you could stay with that brand and look at the Xpulse 210, which will be peppy, comfortable and fuel efficient. If you want to look elsewhere, the Royal Enfield Classic / Bullet 350 or the Honda CB350 models make for comfortable, easy-going machines with a thumpy engine and old-school looks.