I don't know about non-EU nationals, though I know people from the US and Canada who managed to get an EU nationality because of their grandparents and simply used that to avoid worrying about visas and all. That said, the companies will be very helpful if you need assistance with paperwork so you should be fine when it comes to it, though I doubt you'll need the help.
About the language, English will be fine for nearly any tech company.
That said, I'd also check out Berlin and Copenhagen; big startup scenes there.
Never worked in The Netherlands so I can't speak for Amsterdam, sorry.
There's paperwork, but the paperwork is easier when the employer wants you, so defer it for now.
Employment is something else entirely. Skilled migrants can come under the knowledge worker program ("kennismigrant") or the European blue card program. There are a number of websites where you can read about this.
You do have to find a company that will sponsor you, but that's the main barrier to entry. Some Dutch companies want people who speak Dutch, but many will be happy to hire those who speak English. The Dutch government also offers incentives to people coming from abroad where the person pays 30% fewer taxes for the first 8 years in the country.
As an American who's looked into the possibilities, I'd say that the Netherlands is probably the friendliest country in Europe to migrate to. The Netherlands is welcoming to migrants (at least the skilled type), it has a healthy IT sector (with a good number of startups in the Amsterdam area), and English is widely spoken. I'd still advise eventually learning Dutch, but you can at least get along with just English.
Of all the countries in Western Europe I think it is by far the best right now to jump to from outside of the EU.