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I think Ultimate Spider-Man is a good comic for new readers, it was a big gateway for me at least. But going back to it after reading a bunch of 616 Spider-Man you can see how it's like a cover band of all the big moments.
His time with the X-Men was way more egregious. We start with dark alternate future, go to Shi'ar holding Jean Grey on trial, and end with a Proteus clone.