The 2600 is definitely not a bad CPU. But whether or not it is the right choice partially depends on your graphics card. A weaker CPU can throttle high end graphics card performance slightly. A 2600 is competent for gaming on a budget, but the difference between the 2600 and the 3600 for gaming is huge, especially when noting that the latter is just $40-50 more in price.
Additionally, when doing video editing and streaming, there would be a noticeable improvement.
Take a look at this comparison.
Keep in mind that single core performance is most critical for gaming, while multi-core is critical for your other needs.
Also keep in mind that Ryzen is about to announce their 4000 series processors in a mere 4 days. After the announcement, a release is expected in a matter of, possibly, two weeks after the announcement. That means that a 4600 CPU is about to be released, and will undoubtedly be in the price range of the 2600-3600. The performance jump between generations is expected to be far higher than between previous generations.