Well, this is the tricky part. Less intensive means something where you finish your final repeat feeling like you had one or two left in you. Depending on your training volume, this might be 4-6 repeats at 5K pace, maybe more.
As for how high or how long to build your volume, I'd suggest thinking of it in another way. At this point in your running, you need to establish a good base but you don't want to neglect the other aspects of your training for too long and you also want to get in some racing experience. Pick a goal race, maybe in late summer or fall. Then build your training schedule back from that. About a week or so for taper, about 2 months for speed work. Everything before that is base training. Use that time to build as high as your body allows. Maybe it's 40 miles per week, maybe 50, maybe more, maybe less. Whatever is right for you. Next time around, it will very likely be more. Focusing on this time, though, spend your time between now and two months focusing on base. That doesn't mean you never run fast. If you feel especially good, throw in some strides or some other faster running. Always keep in mind, though, that you want to be back out there tomorrow. Keep the fast running relaxed and under control.
Finally, don't run just the goal race. Even while you're building your base, work some races into the schedule. You'll gain valuable experience and you'll be able to see your progress. I've heard from people who, in their first true base building phase, have cut 1-2 minutes off their 5K times in 6 months or less. I wouldn't tell anyone to expect those results but I would say don't be shocked if just base training, over a few months, produces some results. More important though, it will set you up for bigger gains once you add the speed work back in.