(Said with a John Wayne twang ... )
"Hold on there, pardner!!!
Take one step back and no one will get hurt.
Now, drop the search engine.
That's it, now kick it over here.
Nice and gentle like!
Good, now we can talk."
You are, IMO, teetering on the brink of a cliff known as "If only I had better gear". There's a slippery slope at the edge and, if you hit it, you'll go down to the very depths of Dante's fourth circle.
The good news is you are basically correct when thinking a camera with a larger sensor and a lens with a "faster" aperture will allow lower shutter speeds and/or lower ISO values. Though, as TC indicates, if your information comes from reading the internet, this is following a somewhat untrustworthy prophet. The trick prophets use is to include just a smattering of truth and then to lie their rear ends off once you begin believing they are there to help you.
So ... drop the prophet.
Kick it over here.
Good.
One of the first things to realize is, everything and anything you buy will be a trade off. No matter what you buy, there will be a drawback to owning that product.
This applies to pretty much everything you can buy, not just cameras.
Certainly, cost is one of the most significant issues when you begin asking for a camera with better low light performance. Incremental improvements can cost exponential amounts.
Other considerations of overall image quality and ease of use, say, when needed to catch that quickly developing shot, can and probably should enter the picture.
Once you begin thinking new gear is the answer, you tend to get caught up in the web of always thinking more and better gear will be the answer. The pattern then begins where you acquire gear until you either become frustrated by the basic rule that says you must ultimately live with the limitations of whatever you own or you realize everything is a trade off to begin with.
Once you reach that point - or, hopefully, long before - you must realize
the first rule of photography is you need light. The more light you have available to you, the better you will be at taking good photos. More available light means more available options for you, the photographer. If natural light is limited, you need to reduce your list of options and select the most appropriate next best response.
You do not state a reason for not wanting to use flash as a supplement to the available light but this is somewhat irrational once you consider the fact every camera you can buy is still a trade off.
Yes, you can gain faster shutter speeds and lower the ISO value by buying a "better" camera. However, given the virtually constant reductions in available light once you step indoors with your camera, eventually you will find the best next step is to rely on flash as a supplement to your camera's light gathering capacity.
The question then becomes which is the next best option in flash units. Because, if you are not using a flash and you want supplemental light, then your cost again begins to climb. Add to this the fact flash can, for most average photographers, be more flexible in its application than would be fixed lighting fixtures and you find some very good reasons to begin looking at flash units.
O
f course you can do better with a camera that is superior in technical measurements to your compact. However, once you begin to think
you will be better once the gear is better, the chances of you heading down a very dark and dangerous path increase.
It is far less expensive, and generally considered to be the smarter option, to add supplemental light than it is to just buy more camera. Gear heads, of course, disagree with that statement.
If flash would somehow disturb your subject - a child perhaps - then you should investigate other means of setting up your shot. Or, realize everything has its limits and work to discover your next best work around. High ISO values can be resolved in several ways, most of them done in post production. Some cameras offer better than average high ISO performance but they too have their drawbacks;
Fuji X100T Review
That's my opinion at least. I'd say buy a better camera, it will be an investment you do not regret if you purchase wisely. Do not, however, begin to think the gear makes the photograph.
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