Anyone who is promising you you can stay without any extra admin is not able to make those promises at this point, so get yourself covered now, application processing times are dreadfully long as it is.
DorothyL Apply for EEA(PR), you need that before you can apply for citizenship, and if it gets to a point where you NEED citizenship, it'll by then be too late to start the LOOOOOONG process of EEA(PR) and then onto Naturalization.
EEA(PR) will more easily convert to ILR as it's a similar thing
wait and see is so flawed because it could take you 2 years to get through the whole process. So in in 2 years time you're told you need this stuff, you can't just get it, you'ld only be able to START applying, at which point you might not be able to stay while you're being processed.
DO NOT expect the Home Office to allow much if anything in the way of cross-over time. It hasn't allowed any in the past when other changes were introduced with little or no notice.
If it comes to the point where you are required to have a PR card, the attitude you might THEN find yourself up against, is well, you've had 2/3 years since the referendum, it's not our fault you didn't get the paperwork you were entitled to during that time.