On Topic:
The New Republic are absolutely moronic individuals. The political reason given for their military downsizing are not just laughable but almost insultingly stupid. The main reason was that after they seemingly broke the back of the Empire they downsized to reassure the greater galactic public that they weren't the empire and wouldn't be oppressive and controlling. Two problems with that. PIRATES/RAIDERS/TERRORISTS, Ethnic and Species Tensions! You see all those space pirates, illegal smugglers, raiders, criminal cartels, rogue fleets, ect, are still out there, people still have to police the outer worlds, have to protect trade, protect the innocent, fight those who would harm others. But *GASP* you can't do that with a single fleet centered around your capital world! Even if you let surrounding wolds police it themselves, many worlds after decades of military oppression by the Empire won't have the fleets, ships, manpower, or officers to do the job anywhere adequately. And if they for some reason DO have the economic and military power to do this, we come into problem 2 Ethnic tensions between neighboring species and star systems. It was outright stated in many of the EU books that after the empire folded many repressed tensions, wars, and disagreements sparked into full fledged conflicts that the New Republic now had to deal with, quite succinctly in the Thrawn series of books.
Now all of this could be avoided, and the political grumbling killed by one fix. Regional fleets, specifically formed from the previous Rebellion regional cell system which worked amazingly well against the empire, (Which BTW is totally within Disneys new cannon). They have the infrastructure, connections, regional support, manpower, and equipment to handle the job. They only thing that would need to be changed is certain leadership positions to ensure that everyone within the entire command structure are impartial and objective minded individuals to make sure that the previous ethnic tensions don't become an issue.
This would solve politics because under regional rule the local star systems have a say on what goes on in the military structure and can use them as a general impartial policing force.
Next is baffling nature of HOW THE HELL THE FIRST ORDER CAN MAKE STARKILLER IN THE FIRST PLACE WITH NO ONE KNOWING! I mean the Emperor made a star station the size of a small moon and tried his best to keep it absolutely secret. It failed. It failed so hard that the Rebels successful attempt at killing it wasn't even their first time TRYING. Now why the hell is Starkiller not revealed as soon as the plans are drawn up? There are more than enough people in the power structure or simply working on it to have more than enough reason to secretly slip that information to the republic, since there is not a force sensitive powerful enough to latently keep ALL of the First Order under their force control. For reference on how hard it is to keep anything that big secret, Operation Barbarossa was known to be happening by EVERYONE, even the soviet Union, (It was only fucking Stalin who overruled basically everyone that the Soviets were caught with their pants down while changing). Even Operation Overlord was known by the Nazis to be about to happen, and the Allies succeed through brilliant redirection methods and by going in very unfavorable weather, and even then it required a lot of luck and hard work to successfully trick the Germans. So even the New Republic can realize, "Where the hell are all those resources and manpower going? a black hole?" Even the excuse of them using many of their resources from the Unknown Regions have the problem of the fact that the Emperor with the resources of the ENTIRE Galactic Empire couldn't make a station the size of a small moon secret, how the ll is the First Order, an organization a percentile the size of the Galactic Empire, even with the presumably largely underdeveloped Unknown Regions, going to make a planet sized starbase that converts a small amount of the power of a sun, and fires it across hyperspace, a secret?
I could go on, but you get my point. I'm very disappointed with JJ Abrams and Disney for the direction they took. (Of course the Books after the Pellion-Gressom treaty weren't much better, but still).