Forget the heart rate stuff unless you've got some accurate sense of max hr and lactic threshold... then you can probably forget it anyway unless you like playing with those sorts of numbers.
Just pick a ride and ride it. You'll get faster with time and will consider lengthening it but to start with, just pick a ride and stick with it. It's normal to finish a ride feeling a bit knocked around, but that should fade through the day. Feeling tired is a different feeling. You'll feel tired after a ride but if it persists through the day, give the next day a miss so you recover.
As you get fitter, learn to ride hard and fast but also learn how to do a recovery ride - gentle pace, low gears, legs just ticking over at a decent cadence at a low effort.
Oh, and riding a geared bike rather than a fixed gear is a good option too in the early days because much as I love riding fixed, there's nowhere to hide and if you've pushed too hard, you just wind up mashing which isn't good for anything.
All this relates to someone in yours and my condition - fat, out of shape, trying to get back into it. I've got a bit of a head start, which is where the above comes from.