Pushing and pulling - you mean consciously pulling the foot up. If RW said that then I disagree - cyclists don't generally pull up with the foot except for short bursts maybe in sprinting, they just bring the foot up so there isn't pressure on the pedal.
Cadence is subjective - studies have shown that high cadence is mainly to do with lowering peak forces required to go very fast - so the better you are the more sense it makes to ride at high cadence - if you copy lance armstrongs cadence and you are riding at 15mph you are probably not doing yourself many favours.
Turbo trainers are fine if you don't mind doing several hour stints on them - personally I find it much easier to do a couple of hours on the road and you have the benefit of learning bike handling skills too.
I think the first step is to be able to do a decent length ride - say 40 miles, even if you need a cafe stop at first. Get that basic fitness and get confident on a bike, handling it, descending etc so you can start going out with a group.
