I'm not sure who from inside that house killed JBR, but it was definitely a family member, and they were definitely all in on the cover up, with the possible exception of BR (assuming he didn't accidentally kill her). But what was the plan? Great question... A few points:
1 - JR is a CEO. I've spent a lot of time working with CEO's, and most do not believe normal rules apply to them. They do not expect to be held to the same standards as others, and I can see that he would think that the police would believe whatever he says, so long as it's reasonably credible. Again, CEOs are not use to being told they are liars, or treated as criminals. I think he was reasonably sure everyone would accept whatever they say, they would be treated as grieving parents to whom a terribly tragedy had just occurred (more or less what happened).
2 - The Ramseys had no idea the case would turn into a national spectacle. Keep that in mind when examining their actions. They probably assumed they would need to lie to the police, friends, and family for a day or so, then it would just go away. They never in their wildest dreams (nightmares) assumed it would blow up into a nationwide fixation. Again, he's a CEO, he tells people what happened, they believe him, and they move on.
3 - I am fairly sure they were both in on the cover-up. They never slept that night and probably went back and forth on multiple scenarios, changing their minds, panicking, screaming, crying, you name it... There was never any ONE plan, it was a process that evolved/devolved throughout the evening. And sleep deprived adults, after such a terrible tragedy, do not always think straight, so it's not surprising the eventual plan does not make a tremendous amount of sense.
4 - I think they eventually decided to call it a kidnapping, in order to alert the police, but also give them time to get rid of the body. I think they wanted to get the body out of the house in a suitcase and leave it in a secluded area away from the house, but not so secluded that it wouldn't be quickly found. They had hoped to do it the next day or evening. They had no idea the police would never leave, and during the day they realized that it would be impossible to discretely get the body out of the house. So they had to go with Plan B and find the body, assuming a kidnapping gone wrong... Of course that made no sense with the ransom note, but they had no other options. I also think he staged the scene in the house just in case he wouldn't be able to get the body out of the house. He probably thought there was a decent chance he would never be able to get the body out, or that perhaps it would be discovered by police before he had the time to get the body out.
5 - I think JR was overconfident in his ability to control things. He thought he could stage a kidnapping, and when he had more time he would tie up loose ends, discretely dispose of the body. He was sure the police would believe him and do what he wanted, just like everyone else with whom he interacted did what he wanted. He was wrong about the control, but right about one fundamental fact: everyone more or less believed his story, and hence did not secure the crime scene in any professional way. This is what ultimately saved him.
6 - Why not just pretend someone is sick, cancel their flight, and use that time to dispose of the body? Good question. Perhaps they thought it would look very suspicious. Perhaps they were overconfident in their ability to fool the police, file a report, then get the police out and manage things as necessary. More likely they were just not really able to process much, and thought their best plan was to alert the police immediately to avoid any changes in their original travel plans, which would set off red flags with the police.
7 - I think it's a mistake to assume a master plan. My guess is that the first few hours were spent in total shock, anger, fear, you name it, a roller coaster of emotions. The last couple of hours were spent trying to stage the scene in a plausible way to avoid guilt and buy time.