A good run-down of the options you can find here: Second Passport: How to get dual citizenship | Nomad Capitalist
(not that you do not always need a passport or citizenship sometimes residency will do for opening a bank account and tax purposes)
The cheapest options are below, problem is that is dificult to open bank accounts using those residency/citizenship countries! (So I opted not to go that route)
Paraguay (not really a nice place, relatively criminal/unsafe)
This emerging South American country offers a straightforward permanent residency program that allows you to apply for citizenship after as little as three years, provided you make some form of economic investment in the country. This can be as simple as opening and funding an bank account with as little as $5,000. You can also start a small business and pay yourself a taxable salary, or invest several thousand dollars in Paraguayan stocks. Paraguay is an open place where everyone is welcome, and it is one of the freest countries on earth. (you also need to live there a.f.i.k. for a year orso, but that can be 'fixed'. There is a relative large German community they can and will help you (this will cost you 1.500€, but saves you a lot of waiting time and frustration)(use chrome & googlte translate and search for "paraguay + auswanderen")
Panama (a 'relatively' nice place)
Panama’s Friendly Nations visa program makes it extremely easy for citizens of over forty countries to get residency there with a $5,000 bank deposit and one other “economic tie”, such as ownership in a Panamanian corporation. Once you are legally resident in Panama, you can get citizenship in as little as five years.