You can catch Wrasse, Codling, Pollack, Makkies, Coalies...... and plenty more. Not sure of any marks near Edinburgh but St Abbs down the coast is on here in a few reports and looks decent. If you do a search I'm sure you can find a few more.
A standard beachcaster casting between 4-8oz would probably do you with a big fixed spool reel or if your confident enough a multiplier.
Depends if you want to fish from rocks into rough ground or from beaches onto clean ground or a mixture of both.
Do you have a car to travel to marks? If so look for Codhead bobs site. He has loads of marks in Fife that you could try.
Hope this helps a little.