@BrodiePupI don't have a puppy at the moment, but I enjoy lurking on these threads.
So much of raising puppies is down to the luck of the draw. My current dog, now almost 3 years old, was a very easy puppy in most respects and I know how lucky I was! If you're concerned about your pup walking on a lead, I would say don't be hard on yourself. Most things we teach dogs are natural behaviours they would do anyway, but there is nothing natural about walking on a lead. So it can take quite a while to click. I would say begin training in the house and don't even put a lead on him. Just get him used to walking by your side. When he's happy to do that, put the lead on in the house and practice that way. Then move outside to the garden, then to a quiet road, etc. Each training session should be very short at his age, of course.
But even doing all that, puppies can become overexcited when they're out in the big wide world! I remember taking mine on a walk when he was about 5 months old and there were so many people and dogs around that he was overwhelmed. It wasn't his fault, it was mine for putting him in that position.
Also, I always cheerfully ignore the "5 minutes per month of age" thing. It has no scientific basis whatsoever. Obviously, one should never overdo it with young puppies, but my dog would have been climbing the walls if I'd stuck to 15 minutes of exercise when he was 3 months old or 20 minutes at 4 months, etc.
I completely understand what you mean about the constant vigilance. But this stage really doesn't last long. Take heart, your pup will grow up faster than you could imagine. And take lots of pictures, because you will miss his puppyhood someday and want to look back at how cute he was!