I personally use HSBC, you need a minimum of 10000le to avoid any charges, you can have internet banking and you get a cash card which is accepted at most cash machines worldwide, however you cannot use it for normal online or store shopping as it does not have a chip or a security code on the back. They do have a prepaid credit card that you can use for online and store shopping.
I have accounts in LE, Sterling and US dollars, you can also have an Euro account, as long as all accounts combined amount to 10000le there is no bank charges and they are all serviced by the same cashcard, you do not need a seperate card for each account.
So, for example, you could have £600 in your sterling account ,$500 in your dollar account and 4000Le in your Egyptian account and you will not incur charges on any account because they amount to over 10000le in total. They also have a 3 or 5 year bond that paid interest of around 9% last time I looked, much better than any rate that you will get in Europe, if you have the 3 year bond the interest is paid quarterly and if you have the 5 year the interest is paid monthly into your normal account. There is a penalty for withdrawals from the bond but it is minimal.
All you need is your passport, a deposit and to answer a few simple questions to open an account, you can pick up your cashcard and pin number from the bank about 4-7 days after application.