Edinburgh has pretty good transport links but being close to the centre of town is always handy. Most student/summer work accomodation would be in flats in the old stone tenements around easter road, tynecastle, marchmont, gorgie, morningside, merchiston and newington.
You would need an NI number if you want to avoid the dreaded emergency tax...there is more info here
For work going into a local job centre would be your best bet but if you want to have a few interviews lined up before you arrive there are loads of online employment services like http://www.jobsinedinburgh.com/
, or you could try the employment suppliments in The Scotsman, Edinburgh Evening News, etc.
As edinburgh has such a huge student population, you shouldn't have any issue finding accommodation, some of the uni's/colleges even rent out their halls of residence.
Any other questions just shout!