I really enjoyed the film, but the background setting leaves a hell of a lot to be desired. Presumably they will flesh out those thirty years with new canon EU stuff, but just from Force Awakens it can be rather confusing (especially for a pretty informed fan such as us Wookieepedia-ers).
I've only come across vague mentions from Leia's bio that the New Republic has been disarming, believing the Empire to be too weak to try anything and/or willing to stick to the peace treaty they signed. We know from the Battlefront DLC (and common sense) that the war didn't stop after Endor, with that Star Destroyer being crashed into Jakku to prevent capture - damn planet-divers - a whole year afterwards. It could well have dragged on for a decade or so, which could explain why the Republic (presumably larger than the First Order) wants to move on and rebuild the economy without having to fund a vast Mon Calamari fleet etc. Even then, the First Order were apprehensive about openly moving against the Republic, hence their decision to take out the main core with one big pre-emptive strike (while there will still be some Republic remnants around the galaxy, I am sure).
Considering things with a purely "ooRP" sense (i.e. what Disney/Abrams decide to try and make things more popular), the Resistance being so small ("we lost half the fleet!" = a dozen X-Wings) compared to the First Order (who are only seen to have Starkiller base, one capital ship, but a large army) brings the setting closer to the underdog Original Trilogy Rebels, rather than the Republic Fleet and Army of the prequels.
Han Solo dies for inRP reasons as Fallen said, but ooRPly because Harrison Ford isn't really a fan of the series or character and is just in it for the money (hence the huge paycheck and no need to film any more).
I'm a bit disappointed as some have said that it is so closely mirroring the Original Trilogy's plot, with the female lead presumably revealed as another Skywalker and a bad one (even if he is also an Organa-Solo) brought back to the light in the next film or two.
Also for the "only four planets" thing, even Phantom Menace (yeah yeah, not exactly great to hold it up as a good example) which is supposed to be flashier only had Naboo, Coruscant and Tatooine. Attack of the Clones only added Kamino and Geonosis.
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Spoiler
- a whole year afterwards. It could well have dragged on for a decade or so, which could explain why the Republic (presumably larger than the First Order) wants to move on and rebuild the economy without having to fund a vast Mon Calamari fleet etc. Even then, the First Order were apprehensive about openly moving against the Republic, hence their decision to take out the main core with one big pre-emptive strike (while there will still be some Republic remnants around the galaxy, I am sure).