Amsterdam is a fantastic city to visit, as I'm sure you realise if you've been there numerous times, but moving to the Netherlands can be a completely different story. It's notoriously difficult to get a work permit/residence permit for the nation. These are the types of visa you'll need to successfully live and work in the Netherlands, you don't need to get citizenship (which is actually nearly impossible to get unless you marry a Dutchman or woman).
Before you start a business in the Netherlands, without a Dutch or EU partner, you'll need to make sure you have the right residency status. Check with the IND (Immigration and Naturalisation Service) to get a green light. You will have to prove the following: You are qualified to run the business in question, you have a business plot, your business serves an essential Dutch interest, i.e. “extra value” for the Netherlands.
I would recommend consulting with a visa service provider, and asking about self-employed/investor residency permits.
Regarding the cost of living in Amsterdam, it is high. Accommodation will be your greatest expense, and prices are lofty (even for small, poor quality flats). There is not enough supply and too much demand for housing in the city. Expect to pay at least 2000 Euro per month for a small, low-quality place in the city centre, 1000 Euro for a place on the outskirts of town, and as much as 7000 Euro for a luxury place in the centre.
Otherwise though, you'll only need to worry about healthcare, food costs and transportation (all of which you can minimise quite efficiently). Amsterdam is a cyclist's city, and biking is free.
Consult the Expat Arrivals Amsterdam guide for more info.
Congratulations on your decision to move to Amsterdam and start a business :) I think it's great to take initiative like this and flip your life upside down and inside out, it's always a good experience and you'll learn a lot from it I'm sure! I'll try and answer your questions as best I can. For
1) Moving to Amsterdam yes you will probably need some kind of visa. I am a UK citizen so I'm not familiar with the visa process, I'm sure you can google more about this to find out. Once you're here you will have to register for a SOFI (social security) number, which basically everyone who works must have.
2) Living in Amsterdam as the previous person commented, is going to cost quite a bit. The rent prices though I think can be a bit lower, you can find a nice place in the center for something around 1400 or 1500 (and I consider this steep), or if you look in the outskirts it can be around 700. Of course it depends on if you want a studio apartment, or something with 1 or 2 bedrooms, furnished or not, etc. You can search on www.expatriates.com or amsterdam.craigslist.com for private rent offers, or you can go to places like www.funda.nl or www.dekey.nl or www.rotsvast.nl (or many others) which are rental agencies and they will probably ask you 1 months commission upon rental. Public transport isn't super cheap, it costs about 1.20 euro for a 15 minute tram ride, but of course you have the biking which is free! You just have to set yourself up with a bike when you get here which should cost around 150 euros for something good.
3) Starting a business is going to take a bit of paper work but I don't think it's too hard. You need to contact the Chamber of Commerce, and they will help you. There's some good information here: http://www.kvk.nl/english/startingabusiness/default.asp You will also have to sign up for a VAT number, they will point you in the right direction. Not sure about time spans here, shouldn't be too long though. Things move quite fast over here usually. One year would most definitely cover it, and you would have customers by then also :) What kind of business are you setting up if I may ask?
Alright I hope I helped, if you have any more questions don't hesitate to ask
all the best
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