coconut oil is the best oil to use, and it makes the eggs taste super!
As for the other types of eegs, it really is more to do with the heat effects on the eggs that changes their structure so to speak, thus oxidising cholesterol the more they are heated. Since there's more cholesterol in the yolks then scrambling results in more of the yolk being in contact with the hot surface of the pan.
So, soft boiling, frying but leaving yolk runny to runny'ish, poaching to leave yolks runny is ok.
Omelettes will need to be done fast and leave runnyness to the yolk and likely to the egg white.
The best way to take eggs is raw (run hot water for 1min over them before though, as I already mentioned). Not everyone can do that though - except Chong Worrior lives by 'em!
As for the fear of Salmonella poisoning there's always a chance, BUT if you choose free range eggs the chances are greatly reduced. Hens are happier and thusly don't get sick.
Also, salmonella isn't as bad as it's made out to be. It's a relatively benign, self-limiting illness in healthy people.
An obvious tip: smell the eggs. If they smell different to normal or "off" then don't have them.