Citizenships by investment or the so-called "passports for sale" are the quickest way to gain second citizenship.
You may be surprised, but the cheapest options to consider this year may as well be the best ones. Both of these countries are in the Caribbean - Saint Lucia and Dominica and both of them offer citizenships by investment in the amount of $100,000.
By holding a passport of either of these countries you will have access to EU, UK, Hong Kong, Singapore, and other places, while Dominica is increasingly paving its way to Russia and China as well.