What are some actually good budget zoom lenses for Nikon DX bodies that wont break the bank? Ive been shooting with my D7500 and an older D5300 for a few years now and mostly stick to my 35mm and 50mm primes because I love the sharpness, but I just started getting into shooting my kids soccer matches and the primes are just not cutting it anymore. I need some reach but I am totally lost in the sea of Nikon zoom options.

I have a budget of about $350-$400 and I am totally fine buying used gear from places like MPB or KEH if it gets me better glass. I was looking at the 70-300mm AF-P since I heard the autofocus is snappy but then I realized there are like three different versions and I dont want to accidentally buy the one that doesnt have VR since I shoot handheld a lot. Also is the 18-140mm worth it as an all-in-one or is the image quality gonna be a massive letdown compared to what Im used to with my primes?

I have a big tournament coming up in Seattle next month so I really need to find something that can handle fast movement without hunting for focus the whole time like my ancient 55-200mm does. Just looking for something reliable that wont make me regret leaving the primes at home...