I've been searching Google and the forums here, but so far have not come up with an answer.

I just started working out after about 15 years of not doing a thing.
41 years old, 5'9", 169/170 lbs - my resting heart rate is 74 bmp

When I'm on the bike, what heart rate should I aim for and for how long do I need to keep it there? My goal is - other than the fat burning - just a healty fitness level.

I'm also assuming that the cardio work-out is for just that - my heart and lungs, and so it does not really matter if that's bike, treadmill, stepper, or whatever? That would just be a matter of variety to avoid boredom? Is that correct?

And while I'm at it - for the weight lifting - what should I strive for primarily? Number of reps or set or more weight? During orientation I was told to find a weight I could do 12 to 15 reps, no less than 8, and once I managed 15, to up the weight or add sets. What would be the best way to go for max results?

Any input is appreciated.

You should find your RHR decreasing as you become more cardiovascular fit.
There are 2 ways of calculating heart rates.
The straight line method is what you will see on the charts in the gym ~ they're just general guidelines. Formula = 220 minus your age = your theoretical max. Multiply that by .60-.85 depending on what zone you want to be in.
The more accurate method is the Karvonen method.
220-your age-RHR X (.60-.85)+RHR = your training zone
So, as you can see, you could be anywhere from 116 to 163.
If you're doing cardio 3Xweek, try starting out with 137-142 BPM for 30 mins 2Xweek and 152-163 BPM 1Xweek 20-30 minutes. Do this after your weight training.

It depends on your goals, but that's a good place to start.

I'd up the weight before adding sets.