Now that you've recognized how gentle a low heartrate feels I'm sure a conversational pace is totally adequate for staying under your lactic threshold (but if you could sing you're going too slow!)
For a beginner a good tip is just to go a little bit easier than they think they should be going. Once you've built some sort of aerobic base your training should start including intervals and runs that push you harder.
There are two risks in pushing yourself too hard. Injury and over-training.
EDIT: another thing I didn't mention is that in terms of injury you want to give your body plenty of time to build more distance. Most of your joints and other tissues take longer to adapt than cardiovascular. I think this is where people can get into potential injury situations by ramping up too fast. I personally also try to run on soft surfaces (trails etc.) since I find hard surfaces (roads) a lot more punishing.
When biking, it really doesn't help that I have some silly hills surrounding the house. Even if I'm not going all out, a 10% climb takes its toll.