The cheap way to do this is (if you're from any kind of immigrant background over the past few generations, or in some cases far longer, especially if Jewish) -- "ancestry/descent based". Doing the research to find parents/grandparents who were citizens of e.g. Poland, then applying on the basis of descent, is relatively inexpensive (thousands of dollars in research). Ireland is super popular for this; lots of European-Americans are part Irish.

Caribbean Citizenship-by-Investment is about $100-250k but can include spouse/children.

Various permanent residency on the path to citizenships are also relatively expensive (thousands of dollars, some paperwork); if you move there and establish presence, you go through the naturalization process, in some cases fast-tracked.

Spain has some great programs if you're from a Spanish colonial country (including Puerto Rico, apparently...); the citizenship process gets fast-tracked.

Netherlands has a special deal dating from WW2 for US citizens to get fast-tracked to NL.

Turkey has a really cheap (in fees) program -- $5k or so on top of buying real estate at market prices. I personally am not super excited about owning $400k in Turkish real estate, but it has been a good investment in even USD terms (2-3x) over the past few years, from friends who did it. The program used to be $250K buy-in; now it's $400K and potentially moving up.