Here's my take after having carefully looked over your requirements:
I would suggest going for a petrol. Both the pattern and amount of your usage suggest it. And as rightly pointed out, Petrol and Diesel prices are fast achieving parity - given the current difference, I would strongly suggest rethinking your very first stipulation of the vehicle being a diesel. You'll save money upfront for sure and won't pay that much more for fuel over time as you would previously. You might not even have to pay more.
Moreover, despite how good diesels have gotten lately, given your requirement for a nippy character in traffic, a petrol would be so much better. I think the combination of absence of turbo lag and lower price upfront is worth serious consideration.
And now, looking at the other side of the coin, I'd strongly suggest an auto as well, given your usage pattern, location and what I can glean about your less overt personal desires not perhaps overt in the post. I think, and I know it is a broad leap in reasoning, that you will subconsciously hanker for an Automatic soon enough, and then, as Team BHP so wisely tells us, no matter what we tell ourselves, upgrading costs a bomb. Better to pay a little extra upfront for something you need than have to buy it all over again later.
You may think the advice is contradictory between paying less for a petrol and paying more for an auto right now, but an Automatic is a definite convenience, and potential saving on not buying a diesel now may not be realised in the future.
The only downside I can think of is fuel economy - buying an auto for your next upgrade will likely be from a newer generation of cars with still better FE, and conversely, if you bought a petrol auto now, the fuel costs might pinch. I know I'm not much help, but I feel I must present as many sides of the argument that I can see for myself.
Anyhow, bottom line is that I would think that the current use value of an automatic (subjective) + lower upfront cost of a petrol would be the petrol (objective) + elimination of an upgrade-itch just for wanting an auto (objective) > a more efficient auto later + lower running costs of diesel.
And do not forget the way our population and congestion in big cities is increasing - just look at expansion, 2- & 4- wheeler sales - you might need an auto sooner than you think.
So, with AT and not necessarily diesel in mind here are 3 recommendations:
1. What I would do if I was forced to make such a choice - Stretch my budget for the Creta AT. You'd get your diesel + AT. It's really irritating the way Hyundai have positioned the AT variants - the cheapest AT is a diesel
16.5 is waaaaay over your budget and will really hurt - 15.25 for the corresponding petrol AT mightn't have pinched much. But I'd stretch for my needs - you only live once. I know this isn't a good answer because I simply don't know the background of your purchase decision in this sense (after all, that's what we leave out and leave it at budgets). But, without wishing to trouble you with the most common advice of simply stretching your budget, I will still do it. If you can, go for it.
I suppose that just always happens here - If only you just were to spend a little more, there'd be no compromise.
2. Best car within budget with least compromise - Ecosport Trend+ Petrol AT. Within budget. Will last. Good GC. Good quality. Good ingress and egress. A proper TC AT - none of that AMT nonsense here. Cons - Terrible ride (IMO bad doesn't do it justice), largely a 4 seater (don't know how important that is for you).
3. While I don't see the point of you getting a sedan - bear in mind that they barely match the 175mm GC of your Beat, and on top of that, they'll have much longer wheelbases. So, only if you are ready to compromise on what little bit of rough road ability these others provide, you could consider a sedan. Trust me, this comes from someone who very much likes to push through corners and doesn't care for this new trend of SUVs - they lack true off road ability and have all the body roll. But in our country, even people like me have given up on getting those thrills from Sedans (unless you can afford multiple vehicles) - sometimes even reaching a fun twisty road can be a real pain. So please evaluate this carefully based on your own rough road usage - I couldn't glean much from what you've written. The Amaze has just 164mm of GC for example.
Back to which Sedan. Well...
1. I wouldn't recommend the Amaze for all its decent aspects. The ride quality isn't great, and neither is the build. The poorest GC in the bargain doesn't help (every 5mm matters).
2. Ford Aspire. The quality and dynamics aren't up to the Ford standard, but the ride quality is good, GC is liveable. Nice engines too.
3. Maruti Ciaz. The ride quality on this one is really really good. As is the space - your family's "big car" requirement will certainly be fulfilled once they see the interior and particularly the boot. But seriously, this has just about nothing going for it except the ride and space. The AT option, while a TC, is a mere 4 speed, and the engines aren't really up to the mark. Not this one either, unless you feel the ride quality and space are worth the trade-off.
So, to put it in a nutshell:
If you can, stretch for the Diesel AT Creta.
If you can compromise on ride quality, Ecosport Petrol AT.
If you can compromise on rough road usage (or it isn't required that much), go for either the Aspire or Ciaz. The Aspire might be the better overall package, but if you find the Ciaz's performance adequate for your needs, the space and ride quality are
really surprising.
Cheers!
Edit: Have left out many others, but they would matter only once you decide where to compromise. I'm not one of those who'd never consider or recommend Tata etc. There's other good stuff that might fit you even better, but your first need to pick a lane.