Mog - Nope all training should be specific even (or perhaps, especially) base training. One way in which the body adapts to base training is the proliferation of capilleries. The oxygen transfer is made efficient (or not) at the muscles themselves, not in the heart and lungs per se. They are not the limiting point, the muscles are - that's why training has to be specific. You MUST use the same muscles in the same range of motion.
Minkin - I have used Mark Allen/Phil Maffetone's Fat Burning formula to get the correct HR for steady base building. Although faster aerobic effort will be needed in the base (and this is just a base for a base, remember!), this is the sort of pace that is needed now. Just remember that all formulae are guides - you may need to adapt a bit, but don't adjust more than 5bpm unless absoluletly sure. Link - http://vnews.ironmanlive.com/vnews/markallen/1011626750/
Also, Minkin, this WILL train the heart and lungs. The lower end aerobic training will bring all the adaptions necessary - do not worry! There are plenty of elite runners doing most of their training slower than 7min/mile pace - guys who race 10K at sub 5min/mile pace!
When you shift beyond the 1hr a day mark, you will then need to gradually increase HR but only up to 3 days a week - the bulk of your miles should still be this EFFORT level - the pace however WILL get faster.
MOG - if you can't run an 1hr a day, can you run 5min a day? 10min? You probably could EVENTUALLY run 1hr a day, but it may take a long while. It is though, I believe, ultimately an acheiveable goal for almost everyone.