You should get your self a copy of the Spoke Edinburgh Cycle map, it shows all the off road routes and dedicated cycle paths. As well as the which roads are best for cycling and which should be avoided. Most cycle shops in Edinburgh sell them.
I find the routes with bus lanes safer than the other roads. You only need to worry about buses and they tend to be driven by people with more care than the typical car driver. I think that once you get cycling, you will find the Cortsorphine Rd better than many other options. If you want traffic free, the canal towpath from fountainbridge will get you pretty close. But as most have commented - the Spokes maps are excellent.
The Union Canal path is a good option if you really really want to get away from the traffic but the surface does get pretty bad out past Wester Hailes, especially when it's wet.
Avoiding traffic isn't always the best option. If you only ever ride on offroad paths you'll struggle to pick up the confidence to ride on the road. Get out there and mix it up with the cagers.
Corstorphine Road is probably one of the least stressful road routes in Edinburgh. Nice wide road with bus lanes all the way out to the Gyle, and I've found the Lothian Buses drivers to be really courteous. I don't think you'd have too much trouble.
Judging from reviews the Marin is a good bike but for £400 I'd rather have a Specialized Sirrus. The Revolution does look good at £250 though. I looked at getting a Courier Race last year for only £30 more but unfortunately the money had to go on other things. They only have a single front chainring, which might limit it on really steep hills, but I guess only you can decide whether this would be a problem.