Just because it has 256MB of RAM doesn't mean it should sit in the trash....mine still works just fine and is used daily alongside my third gen iPad. @OP, a refurb first gen iPad should be enough to browse the web, email, and Youtube [as you stated before]. If you can find a refurb iPad first gen, get it and have your family use it whilst you use the Touchpad.
The original iPad will work very well for what you say it will be used for. Obviously the newer models have some technical advantages but if that is not important then the original or the 2 will serve you well. One thing to keep in mind is that Apple has a way of phasing out support for older hardware over time; a two year old model is two years closer to that point.