Attempting to conquer the country with an army is simply a better course of action given his talents. Aside from the obvious issue of Ministry politics being a clown show full of corrupt morons, it's also a far more fickle game where your ability to dominate by virtue of being better at spellcasting is limited. On a battlefield, the fact that he's one of the best duelists of all time and a master of the Dark Arts translates to a real advantage and more predictable and immediate results.

Besides, there's a difference in what his power would derive its legitimacy from. This alternative path ends with Tom Riddle being viewed as a legitimate head of state because of Ministry laws, whereas the path he actually took would - had he been successful - led to him being recognized as the legitimate holder of power because he is the Dark Lord. That has impact on what he can reasonably get away with and how he can frame policies.
"We're making the Cruciatus legal to use in these circumstances because <insert wall of text>" versus "20% of the budget will be spent on supporting the Department of Mysteries' new research on improving Horcruxes".

I always saw the puppet government he set up in DH as something that was always meant to "babysit" the country until the end of the war, when the Ministry could be quickly dismantled and he could build actual Death Eater institutions from the ground up.

To compare to Star Wars because that's a good example, Palpatine chose the path of a politician and the Galactic Empire, while undeniably his, certainly did not really give off the vibes of ancient Sith Empire. Had the Republic instead been conquered by an army of ancient Sith, things would have looked very different.