OP to answer your questions there are several ways to reduce noise:-
1. Change your exposure settings (aperture and/or shutter speed) to keep ISO low, the lower the ISO the less noise there'll be (although available light will also affect noise)
2. If you can't change exposure values (ie at widest aperture and taking moving subjects so can't lower the shutter speed) then use flash, preferably bounced/diffused flash from a speedlight rather than on camera flash.
3. Upgrade your equipment by buying and faster lens and/or body that has better noise handling.
In terms of what an upgrade can offer, this has been mentioned already but
generally it is more/better functions, better AF, better sensor, better build, possible weather sealing, different ergonomics and possibly a few other things.
Now for my opinions. Everyone's tolerance of noise varies and if you don't like it then that's all that matters and it shouldn't matter if others think noise adds character, or shouldn't be an issue etc. Just because someone else is happy with noise it doesn't mean you have to be. However, keep things in perspective and focus on technique before throwing money at new gear hoping it's going to be the answer to all your woes. And as mentioned, we pixel peep which magnifies noise, when viewing at normal sizes noise will be far less apparent. Phil's analogy of the Mona Lisa is a good one.
The D7200 isn't the
best handling with regards to noise, but it's pretty darn good. Yes the D3200 is good too, but with the advancement in tech when you start getting up to 3200 and 6400 ISO the difference in the newer cams is more apparent. At 6400 the D3200 is pretty bad/unusable IMO.
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OK, test charts etc aren't the best test and aren't a true reflection of the real world (especially as chroma noise is well managed by LR etc), but they do give a reasonable comparison from one camera to another.