That bike is fine for your style of riding.
Sounds like a tune-up is all that's needed to get the shifting right.
As far as upgrades. The most significant thing you can do is upgrade your fork. Bar none that will have the most dramatic change.
From there, I'd just replace parts as they wear out, or they go on Clearance Sale!
A quick tune up will get the shifting working right, as mentioned, I'd learn to do it, so then you can fix it on the trail if it breaks.
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