I need recommendations for a good camcorder for soccer games.

Are you trying to record the whole game or a single player?

Probably the most, "well-balanced" camera you can buy for <$1000 is:
Sony ZV-E10 II

Not cheap, but sony has the best bang for the buck and a wide range of lenses to get you going.

Be warned. When you start looking at lenses you can quickly get up into the big bucks. I'd start with a 16-50mm lens and see if that does enough for you. Can get one with a camera for just over $1000 together.

Was looking around on Amazon, and there's a sony 55-210mm lens.
55-210mm lens

It's only $300 for the lens, and would undoubtedly give a lot of zoom for most sporting events. Probably worth a look if you're getting more serious about it.

The price can quickly go up from there though. You can easily spend several thousand dollars on a good lens.

Thank you so much. That was very helpful.

I'll preface my comments by saying I've been the photographer/videographer for my kids MTB team for the past 3 years and I'm responsible for the team photos and the end of the year video/slide show. So I have a little experience on the subject. ETA: I've not only studies the options online, I've actually USED them in these sorts of situations. I've also been in the Sony A mount and E-mount ecosystems since 2009.

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Probably the most, "well-balanced" camera you can buy for <$1000 is:
Sony ZV-E10 II

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So you're really going to recommend a camera with no viewfinder for shooting outdoors in bright sunlight? I'm not sure that's a good combo.

You almost got it right though. The real answer is the A6700 or the little older, but still capable A6400. Both come with a digital viewfinder. The A6700 can do 4k at 120 fps which means you can really slow the action down.

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I'd start with a 16-50mm lens and see if that does enough for you.

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What?!? Wrong answer. You'll never get the reach you need with only a 55mm on the long end (83mm equivalent). In fact, it would likely be a worse solution than the iPhone. I know because I have the same lens. The only time I ever use it is when I set up my NEX-7 on a stationary (unattended) tripod and let it roll video. The real answer here is the Sony 18–135mm f/3.5–5.6 OSS. That gives you a functional equivalent of 27mm-203mm. That should be more than enough range on both ends to do what you need it to do. What you don't want to do in an action filled games is change lenses and miss the action. However, the A6700 with the 18-135 would be more than your $1000 budget. Given that limitation, get the A6400 and don't look back. Should be able to find one in that configuration online for $1000-$1100.