Cant help you with places to live or work im afraid but will give you some general advice.
Id say Edinburgh is probably the most expensive place in Scotland to live. Not quite as bad as London yet but prob 2nd in the uk for expenses. Could be wrong on that though but sure I read that somewhere. Flats in or near the centre will cost a small fortune to rent. Prices have sky rocketed since the Parliament was set up due to the influx of government jobs. Im sure there are areas popular with students and the like but I have no idea about that.
It is a beautiful historic city, it still overwhelms me when I come out of the station and look up at the castle. In my opinion it puts London to shame which in my opinion is a dirty, pretty grim and very impersonal place- Edinburgh is the opposite. Sure some people would disagree with that but Iíve never been keen on London.
The weather in Edinburgh isnít that bad, wont be that different from London despite what people think. Not quite as hot in the summer and yes it will rain but nothing that major. Certainly not a reason not to go there.
There are a lot of backpackers there so you wont be short of like minded people to hook up with and maybe find a flat with. I met some aussie guys in Berlin who lived in Edinburgh - and they absolutely loved it. The place is pretty hectic during the festival in the summer but its alot of fun. And of course there are the Hogmanay celebrations to look forward to.