How fast do you have to get to a certain level? Mostly that's not a question that needs any answer. But if you have to get to some level fast, you need a coach. Just so someone will be telling you what needs doing and won't consider your excuses for not doing or performing well when done.
Generally time and distance in quantity goes far in getting you into shape. But it's a process that may take a half dozen years to get you feel confident around other decent cyclists. One of the things that riding longer than two hour rides does for me is makes it apparent how small amounts of energy saved here and there during the first hours of the ride come in handy for performing and looking good among others at the finish.
HR, power and other things just give you a reference in conversations to describe the amount of effort in a more comparable way than just saying "I rode hard up that hill" So just pick a method of HR and use it. In the end, if we defined our zones correctly using the method we chose, then those zones will be close enough to any zones that another correctly set using a different HR method.
I like the concept of functional threshold heart rate FTHR which some consider your lactate threshold power LTHR. I myself call it LTHR but worry that the sticklers will come out of the internet and scream you can only find your true lactate threshold in a laboratory. Which technically is correct, but in the world of HR Zones and how accurate they are, the simple non-laboratory way to determine your FTHR/LTHR is good enough and close enough. <grin>
LTHR zones are simple to figure out. The process is much like finding FTP which also has several methods people argue about which is better. Joe Friel's methods are what I used when I set mine long ago, though I've not been in training mode for a long time as for me with little goals, I've found that quantity of riding works wonders. And have time to do it. Though embarrassingly some sure ride a lot more than me and still want more performance. I guess I'm not super competitive, though I do consider someone ahead of me someone to catch up and pass.
https://www.trainingpeaks.com/blog/j...setting-zones/
https://www.cyclingweekly.com/fitnes...%20minus%20age.
https://joefrielsblog.com/a-quick-gu...-setting-zone/
You'll notice he set 7 zones but the two extra are in the typical zone 5 range of other methods. So I just set 5 zones on my Edge 500 and when it maxes out the upper end of zone 5, it reports it to me on the bike as zone 6. Don't remember whether that means I'm 5b or 5c. But I never did any training to the extent I needed that division in the upper end. For times I do, I'm looking at actual HR numbers in real time while on the bike anyway.
For those of us that don't compete, I think just riding lots and also doing intervals (no planning needed) of all out effort go a long way compared to any formal plan. What comes as you get experience is the same thing that probably makes the difference in really good pro riders..... besides their coached training. They are aware of the results of burning x amount of energy in this moment and how that affects the amount of energy needed to perform at a certain level immediately after expending that energy and also what it means for the energy at the end of the ride.
Hill climbing isn't too magical either as long as you know how to shift to a gear that lets you put out power you can maintain. Hill climbing just gets better over time and repetition and energy you learn to save while getting to the hill. It does help when you finally get to being able to maintain 16 mph or better all the way up a hill to stay a little more aero as you do so instead of sitting up as I was in a bad habit of doing.
If you do need a formal plan to follow with your rides, then read through Joe Friel's blogs, stuff on Training peaks site and other magazine sites like cycling weekly.