To answer your three points in sequence I will rely upon the Freedom House Index to measure both 'democracy' and human rights, the Human Development Index to measure 'Technology & education,' nominal GDP per capita for wealth, the Gini coefficient for wealth disposition and equality.
It is worth noting that petro-microstates (i.e. small countries that get a lot of money from oil wealth, like Brunei or the U.A.E.) have resources that skew the outcomes significantly. Basically, if billions of dollars of oil wealth flows into a country with a small population it can buy development and prosperity, even in the face of resistance from their social structure. Since 'be oil rich' isn't a viable prescription for most countries, tt is therefore worth showing where the top petro-state lies in each measure, and where the next highest non-petrostate lies in order to demonstrate the relationship between democracy and prosperity or 'success.'
In some cases, city-states also have advantages due to their size. When a city-state like Singapore is the most advanced, I will also include the most 'successful' nation-state.
Technology and Education
The most advanced state on the Human Development Index which is considered 'Not Free' by the 'Freedom in the World index' (i.e. 6-7) is
Brunei, a petro-state at number 31. There are 6 petro-states with a very high human development index: Brunei, Qatar, Saudi Arabia, UAE, Bahrain, Kuwait The highest ranked non-free, non-petrostate are Belarus and Russia tied at 50. Russia, in many ways is also a petro state, so Belarus is really it.
Using GDP per capita, the highest non-free country is Qatar at 3 or 4, depending on the measure you use. The highest non-free, non-petro state is Kazakhstan. Notably, Kazakhstan is actually below the global mean for nominal GDP per capita, meaning every single non-petro state, non-free country is below the global average.
Wealth Disposition & Equality
Using the GINI coefficient from the World Bank we can see that equality and disposition of income is more of a mixed bag. Belarus, a not free country, is the #4 most equal country (i.e. with the lowest GINI coefficient), but the other top 10 are all Democratic. South Africa, a full democracy, is also the least equal country.
For this, we'll have to split apart the Political Rights (democratic) from the Civil Liberties (human rights) in the 'Freedom in the World Index'. Not one country which has a 6 or 7 for Political Rights has above a 5 (out of 7) on Civil Liberties. There are 17 countries which have a 5, which is still a bad human rights record.
As a side note, Freedom House has been accused of having a 'house bias' in favor of U.S. allies, but since the conclusion of the Cold War, there is much less evidence of that effect, simply because it isn't clear who is and who isn't allies with the U.S., and in cases where it is clear the countries in question are either unambiguously free or not-free.
You have mostly been taught correctly. If an authoritarian country has oil—or hypothetically some other major source of resource wealth—it is possible to create good economic outcomes for your population. Other than that, however, non-free countries are essentially never in the top tier when it comes to prosperity and rights by any meaningful measure.
The only area where there is any sort of parity is in equality, and due to the relative poverty that non-free countries find themselves, being equally poor does not seem like much of an achievement.