The search for Luke had nothing to do with the Starkiller plot, The First Order had been planning the attack on the New Republic for what we can assume was years or however long it took them to build the base in secret. The First Order seemed to consider finding Luke a side show, a possible threat that could harm them at some point in the future but not their main concern. Rather, the destruction of the New Republic and the Resistance seemed to be their primary goals.
Like I said the Luke searching premise does not flow organically as does the Death Star plans in ANH. The fact that R2 literally just decides to wake up at the end and give them the missing piece is proof of this. It's completely unconnected to everything they had just been doing.
Have you seen this movie?
Literally after they escape with Jakku with BB-8 on The Falcon there is a scene in Snoke's chamber where he is pissed that the droid is going to get to The Resistance because they'll find Luke and Luke will come back and re-establish the Jedi order, up until that point they'd been operating quietly, now and Snoke literally says this:"Our strategy must change" that;s when Hux says the weapon is ready and they decide to blow up the Senate, that was their plan B, because now everyone knows they exist, they committed an act of war that exposed them for what they are in order to try and stop the Resistance form getting to Luke, they are that terrified of him.
And then after Ren fails to acquire BB-8 because he thinks Rey is enough and she escapes they go to yet another chamber conversation where Hux reems out Ren for not getting BB-8 as well and tells SNoke that the droid is probably in the hands of the Resistance, And thus Snoke declares and again I quote "The Resistance must be destroyed before they get to Skywalker"
Amazing that you missed two blatant expository sit and talk scenes that spell out exactly that the quest to findi Luke is the centre of everything.
Why they tell Ren to not let his personal feelings interfere is that Snoke and The First Order would settle for destroying BB-8 and thus stopping Leia from finding Luke even if it meant never finding him themselves, something Ren doesn't want, he wants to find Luke,
The ends result is Snoke and The First Order are terrified that they will find Luke bring him home and he'll re-start the Jedi order. They were so terrified that they blew up the fucking Senate to send a message and thus exposing themselves and then put their entire weapon at risk by targeting Leia directly,
It was all to stop them from finding Luke. They literally say it twice, like not even implied but flat out said twice in plain english during giant exposition scenes, they attack the Republic so as to weaken the Resistance so that they can stop them before they reach Skywalker (literally paraphrasing Hux here) and then they try to launch on The Resistance base because if they don't wipe them out fully right away they will get to Skywalker. Everything they do is about stopping them from getting to Luke, because they don't want the new Jedi to rise.
So I say again did you actually watch this movie?
Tl;dr the entire movie takes great pains to paint finding Luke as terribly important and the reason everything that happens in this movie happens. He is set up as the ultimate fear of Snoke and The First Order and they are willing to do whatever it takes to stop Leia and co from getting to him. In short Luke is the ultimate badass in this movie and all he had to do was stand on a cliff and facial act the shit out of his one scene.
ANH stands on its own resolving it's entire central plot while leaving room for a sequel, Empire was the only film to end on an obvious cliffhanger but it was the second act not the first act to a new trilogy.
The central plot of this movie was finding Luke and omg what was resolved at the end? They found Luke.
Also A New Hope was designed to stand alone because there was no actual guarantee of a trilogy, nor was it even fleshed out at the time (I mean hello Vader was not Luke's dad until a revision of the ESB script). Ergo it had to fully stand on it's own, TFA is literally part of a guaranteed trilogy.