Part of anyone's financial map is a bank account and most expats will choose an offshore account to complement their domestic bank account or for their sole use. Your current account is where you’ll have your salary paid into and pay your various bills and monthly costs from. This means you’ll need Internet banking and at least a debit card. The other reason you might need a bank account is for your six months cash buffer.
It’s essential to keep six month’s costs in cash or a cash-like investment, for example a three month fixed deposit. If you decide to take advantage of your banks deposit offerings for this money, they’ll normally open you a parallel account for this; you should be able to see both accounts using your online access. 
It’s important for your bank to be safe, but realise that nothing is completely safe and that you shouldn’t be keeping too much cash in the first place. Remember that the safer the bank, the worse the deal will be – you’ll get poorer interest rates and you may even be charged a fee. On the other hand, looking at banks with the very best deals may get you burned. Try and find a bank that needs your money but isn’t desperate for it.
Choosing a jurisdiction isn’t that major an issue. Once you’ve found a bank that’s suited to you, if it has a good reputation, it’ll normally have chosen a jurisdiction with a good reputation too. Banks on the Channel Islands are often used since they conform to the UK’s banking etiquette with good levels of client service, English speaking staff, and all the normal offshore advantages of tax efficiency, confidentiality, diversification and international access. Typically you can obtain a bank account in multiple currencies, which makes it easier to organise your life if, for example, you earn in US Dollars but still have a Sterling mortgage back at home.
A better option, if you’re looking to save your monthly excess offshore, is to choose an offshore savings plan. These are structures that are paid-into on a regular basis with each payment being invested into a portfolio of underlying investments, primarily mutual funds. These sorts of savings plans are often used as a tax-efficient pension plan, and have the advantages of total access on maturity (no annuity to buy, you just get all your money), tax efficiency (your money grows within a tax-free structure and can be flexibly handled to maximise tax efficiency on maturity), confidentiality, inheritance simplification (avoidance of forced heirship laws in some countries) and inheritance tax mitigation, especially since many of these plans can be wrapped in Trust.
The best plan if you are considering this is to contact an IFA who can help advise you on how to best utilise these options.