Based on what I’ve read from Reconstructionist authors themselves over the years:
Economically, probably laissez-faire with a strong dose of crackpot. Not much “burdensome economic regulations” but probably also no labor unions or other worker protections, maybe attempts to use the gold standard. Economically, this could result in anything from a kind of exploitative go-go capitalism to an economic basket case. (I really don’t know what an attempt by a modern society to use the gold standard would look like. And if a faction came to power that tried to impliment Old Testament Sabbath laws on a modern society–even “Scary Gary” North though that would be a really, really bad idea.) A factor hampering the development of the go-go capitalism model would be fears by would-be investors and entrepreneurs of being put up against the wall and shot (or stoned to death) for ideological reasons. Which brings us to…
Politically and socially very repressive. Maybe not to Saudi or Taliban levels with respect to women’s rights, but at least as bad on that score as Iran under the mullahs. (Homosexuals are obviously up against the wall.) Probably fewer rights for religious minorities than in Iran, where (except for Bahais) religious minorities have an officially recognized status and a (highly circumscribed) place in the political system. In a Christian Reconstructionist state, non-Christians would likely have no rights to participate in the political system (with “Christian” and “non-Christian” being subject to definition in a highly politicized process in the framework of a theocratic state, likely a dictatorship or oligarchy). There would be a laundry list of capital crimes (apostasy, adultery, blasphemy, idolatry, sodomy, witchcraft, along with murder, rape, and kidnapping) which would produce a repressive effect, but the one to watch out for would likely turn out to be “idolatry”, which can be defined as anything from pretty literal worship of statues, to a quite flexible idea of putting anything before God. Even mainstream Christians tend to define idolatry fairly expansively; the problem with the theonomists is that they combine this with wanting to make idolatry a capital crime. In that event, idolatry would run the risk of becoming the Christian Reconstructionist equivalent of a Soviet state’s “counter-revolutionary”.
All of this could lead to a repressive police-state-style theocratic republic; or, if things went in a slightly different direction, you could wind up with more of a Mao-style “Cultural Revolution”, with local cell groups or neighborhood committees (based on Old Testament notions of rulers or elders over small groups of families., e.g. Exodus 18:21) running amok in an attempt to purify society of all traces of “idolatry”.
Exactly what would happen would depend, obviously, on the specific personalities of the rulers in this hypothetical Christian commonwealth, but also on the circumstances by which it came into being (because, honestly, it’s really hard to see how a Christian theocracy ruled on a late 20th century interpretation of Mosaic law is going to gain power anywhere on Earth).
There is a fundamental fact about Christian Reconstructionists: They want to criminalize disagreements about theology; to make them capital crimes, in fact. And they have that expansive view of theology that dates back to at least the 1980’s and the American Religious Right–competing religions to Christianity are defined not just as the obvious (Hinduism, Islam), and potentially segments of Christianity that are considered to be not true Christianity, but every sort of “ism” from Marxism to Secular Humanism to “Evolutionism” gets branded a “non-Christian religion”, hence idolatrous. This sort of thing is bad enough if you’re talking about school curriculums and textbooks, but if you set up a society where non-Christians can’t vote, and face the death penalty for publicly propagating their faiths (or “faiths” in the case of things like evolutionary biology), it’s not going to end well. Either a police state, a Christian version of the Cultural Revolution, or both (together or in sequence).