As pointed out in the comments, you cannot work under B-2 status, and accepting an employment offer while physically present in the US will most likely violate the B-2 visa requirements, because it is a non-immigrant visa and you had to prove that you intend to return to your home country.
You cannot qualify for an H2B visa, because this is designated for jobs that are seasonal in nature (tourism, construction, etc.), and Web-development would not count as such. The only viable option is to get a H1B visa.
The startup will have to hire lawyers to file applications for the H1B visa for you while you will be back in Denmark, so they don't have to have a legal department. The cost of sponsoring the H1B includes application filing fees and attorney fees. According to http://redbus2us.com/h1b-visa-2017/, "the H1B filing fee can vary anywhere from $1,600 USD to $7,400 USD + Attorney Fee", where immigration attorney fee is usually in the range of a few thousand dollars. Note that you cannot pay any of these fees yourself.
Finally, once they pay the filing and attorney fees, your application will be entered in the infamous H1B lottery. The yearly quota for H1B visas handed out is 65,000, and, just for reference, in 2016 there were over 200,000 applications. If you don't get selected, you may re-apply the following year, but your company will have to pay all these fees again.
Quick note: you do not necessarily need to have a degree. Proving that you have enough experience that would be equivalent to obtaining a US bachelor's degree is enough. See "Can I qualify without a bachelor's degree?" at https://www.uscis.gov/eir/visa-guide/h-1b-specialty-occupation/understanding-h-1b-requirements
You mentioned Green cards. You cannot simply apply for a Green card with no history of being in the US. After 3 years of H1B status you may apply for Permanent Residency (Green card), or you need to marry an American. There are other ways, but most people don't qualify (for example, getting a Green card after being granted asylum).