I have a Chromecast, Amazon Streaming Stick, and a Roku 3 (non of my TVs are smart by default). Hands down I use the Roku 3 the most, but that might just be because of which TV I have it hooked up to. However, I also feel the Roku 3 is the best. The speed of the device, the overall experience, the quality of the streaming, etc. all of it is top notch.
The Chromecast is good, and if you only have basic needs for it, it'll serve you well. The only way to control it is with your tablet or phone, and while that's a good thing in theory, it's not as comfortable as the devices with a dedicated remote where you can do everything by feel rather then having to look down at a device to see where each button is. If you're interested in a Chromecast, I believe if you buy one by the end of the month you'll also get a $10 credit for the Google Play store. Also, I believe BestBuy is doubling the credit and giving a $20 Google Play store credit with the purchase of a Chromecast. It might have ended last week, or it might be going until the end of the month, it's worth looking up if you're going to get a Chromecast.
The Amazon Streaming Stick is also decent, I probably use this the second most, but again that might be based on which TV I have it connected to more than the device itself. However the biggest weakness of this device is it's interface. I don't understand how a company like Amazon continually puts out products with user interfaces that are more "good enough" than great. Interface aside though, I find that it loads videos faster than the Chromecast, but slower than the Roku.
I've never used a Roku 2, so I can't compare it to the ones I listed above. But if I had to buy one device and I wanted to balance options/functions with price. I'd go with the Amazon Streaming Stick. Because I only use a few streaming services, once they're installed and used they're listed with your recently used items which is where the interface defaults to when it wakes up from sleeping. So I don't have to use the Amazon interface much, just wake up the device and select one of the apps that I recently used and start streaming. It also makes access to Amazon Prime videos very easy if you have an Amazon Prime account.
That's my opinion though, you may feel differently. And if you're sure you're just using it for Netflix and YouTube, then the Chromecast will serve you well. Even if you want to expand beyond those in the future, it'll continue to serve you well.