Minimum Budget for Upgrading from Panny LZ8 & Redmi 1s

You are a little constrained with the zoom requirement and the budget. Because if you had a little more to work with you could get a entry level USED (Nikon D3100,3200 or 3300 or the Canon equivalent) with a Prime lens for about 20-25k. Shoot RAW with that and between some minor lightroom adjustments and the ridiculously good aperture of a prime, you could get some fantastic shots even in very poor lighting. I use the combo of a D3200 + 50mm lens currently and it beats every camera phone I have used and both the P&S I have owned.

You could get the same DSLR with a zoom lens for about the same price but I wouldnt really recommend it. For one, its not really compact in any sense of the word, a 50-200mm lens is a pain to lug around. And you cant really shoot zoomed in at low lighting anyway because you just wont be able to keep the shutter steady enough (and a Tripod sucks for anything except static photography). Lastly, the low light performance for most starter zoom lenses is very underwhelming.
 
Sorry for the late reply. Didn't realize you had posted.

...... USED (Nikon D3100,3200 or 3300 or the Canon equivalent) with a Prime lens for about 20-25k. ....

At that price point, I'm not really saving much over an RX100. It will have as fast a lens as a prime lens. It will also have some limited zoom, be portable & less intimidating for others in the family & passers-by. The downside is the smaller sensor & consequently poorer IQ. But I'm not too concerned about that since the RX100 is good enough for me & I'm really not going to pixel-peep.

In any case, I've put this purchase on hold. I'll probably wait until my LZ8 P&S gives way, &/or I feel I'm financially well-off & can justify spending 25k+ on a cam. As things stand, I feel it's probably a better idea to rent a camera to supplement what I already have.

Again, thanks to all for their time. Much obliged.
 
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