Good answer, Dub.
When you say "PR" I automatically think of a 1-rep max. You are talking about hitting sticking points in your lifts, maybe a 5-rep max. That's a little different. What I said about rest periods isn't different.
I think that your real questions is why am I sticking, and what can I do about it? The common explanation is that a beginner gets to the point when he or she can't recover properly from the workout in a couple of days, and needs to "periodize" their training, that is, break up training in a way that works certain muscle groups on different days, and in different ways to allow better recovery. The theory is actually a lot more complex than that, but I think that's good enough for our purposes here. You touched in this when you asked about "a weekly progression" rather than a "daily progression". The answer to your question is yes. Doing heavy-medium-light is one way, but splitting is probably a better way for now. Common ways to split for your stage of training are upper-lower or push-pull-lower. That would mean doing your upper body lifts on one workout, then the lower body work in the other. The second would involve doing things like bench and military one time, chins and rows another and lower body on the third.
There's one other thing to think about. When we decide that we are going to do a fixed rep-set scheme, we limit the ways in which we can make progress. So (for instance) if you've decided to do 3x5, sets-across, the only tool that you have available is varying the weight. So you pick a weight (however you do that) lift it for 3 sets of 5 reps (I'm assuming appropriate warm-up) and then go on to the next exercise. Next workout, you increase the weight and lift it for 3 sets of 5 reps. You continue until you can't get all the reps then feel discourages, or you reset, or ask the guys on a forum for ideas to continue progressing.
Many times this plateau comes because your are adding weight faster than you can gain strength. Simple as that. You don't need tricks to break through the plateau, you just need to increase your work at a slower rate. But if the smallest increment you can use to add weight is 5 pounds or 10 pounds, and you insist on lifting 3 sets of 5, that can be more added work than you can handle.
Why now start out at 3 sets of 3 at a weight that is challenging, but not pushing failure? Then next workout, add a rep or 2. Maybe a set of 4, a set of 3 and a set of 4. Or whatever. Or a 2 sets of 3 at the current weight and 1 set of 3 slightly heavier. That way you can add a smaller increment of work each time. On a given day, if you are doing well, you could even add a 4th set. Gradually you'll find yourself doing a lot of reps, maybe more sets than you feel is ideal, and maybe can't push the weight any more. Then your "reset" is going back to 3x3, but at a significantly heavier weight than you used last time. Not going down to an over-all easier workout.
Does that make sense? I personally think it works better than sticking to a fixed combination of reps and sets. We often have discussions here about the advantages of high-rep, low-load vs. low-rep, heavy routines. This lest you vary it gradually over time. You start low-rep (at least relatively) and heavy (again, relative to you), and gradually shift to a high-rep routine, where the weight is more than where you started, but may now be light for you, at least sort of light. Then go back to a challenging, low-rep routine, and again let it evolve over time.
This also has the advantage of being adaptable to how you are doing on a given day. If you are tired from lack of sleep, or from illness, or if it's just a bad day for unknown reasons, you can go by feel, and not make any big increases. If you have a day that is especially good, you can make bigger increases. Be careful, though. I have a problem with temptation, and sometimes push all three parameters (weight, reps and sets) at once. Sometimes that's the right thing to do, but sometime I end up exhausted and beat-up, and don't do well for a couple of workouts afterwards. Go by feel, but stay smart.
Yes, Dub's explanation of microcycle is right. My microcycle is 4 workouts, spread over 9 days. It's kind of odd, and doesn't fit with lifting only on certain days of the week, but it works for my situation. A microcycle can be as little as 2 workouts, but would rarely be more than 5. You can also think in larger time periods. Terms like mesocycle, macrocycle and just cycle get used, but they aren't too useful to most of us. I organize my training into "cycles" of 4 microcycles, but that's just arbitrary and is for my convenience. For things like "5/3/1" it's more meaningful, since each of 4 microcycles is a little different.
Our greatest fear should not be of failure, but of succeeding at things in life that don't really matter.--Francis Chan