Firstly, Poland can go with any ideology in the mod.

The monarchy stays if you elect the starting marlibs, if you appoint an authdem government in the elections or if the soccons win the elections. The way that works is that the combined support of monarchists+nationalists is what counts for the monarchists winning the elections, with the soccon wing of the nationalists taking over if their support is higher than that of the monarchists.

The republicans get elected off the back of the combined support for the republicans+socialists, and they will make Poland into a progressive, secular republic. The soccon wing of the nationalists can also take over if they have more support than the Republicans when you attempt to pass secularization.

The natpops are a civilian dictatorship under Adam Doboszyński, not a military junta. You get them by not electing the soccons and then fulfilling the requirements put forward when you mouse over the mission Anti-German Agitation. This mission appears after the 1938 election. The set of conditions that isn't reliant on how the AI performs in the war is: nationalist support at or above 50%, be at war with Russia, your government must not be soccon. Soccons can also take power in this path as the moderate wing of the nationalists if Doboszyński fails to consolidate power.

The totalists are obviously a dictatorship under Kazimierz Zakrzewski, the other ideologies are pretty much the same flavor of socialist republic, though you can decide if you want that republic to be centralized or decentralized and so on. The requirements for the socialist uprising are laid out when you mouse over the mission Revolutionary Mood Spreading which appears after the 1938 election. The set of requirements that isn't reliant on AI performance in the war is: socialist support at or above 50%, and be at war with France.

The one ideology that is more of a military junta are the patauts under Marshal Rydz-Smigły, who can coup the soccon government in Operation Parasol, which has the following requirements: nationalist support at or above 50%, has completed the focus Moral Education, has not completed the focus Reinforce the Parliamentary System, faction leader is at war with Russia.

A final note is that you won't be able to do either Operation Parasol or the nationalist uprising if Russia turned socialist.

All of these paths are fun in their own way, so I'd recommend trying them all out eventually.