Hi and welcome! London resident here full of hints and helpful (?) advice.
Areas to avoid depends on what kind of London experience you are hoping for! But assuming you want to live in a safe area, definitely stay away from Brixton, Hackney and most of the east.
A one bedroom flat in a good area will probably cost you upwards of £200 per week, although if you are prepared to live a little further out of town it could be cheaper. If you and your wife are willing to consider a flatshare you could halve that. (Quite common in London for young couples to share flats with others).
A good site to look at for an idea of areas and rentals is
www.findaproperty.co.uk I have personally lived in several different areas of London and I can recommend North/North West areas such as Hampstead/Camden, Maida Vale/Kilburn, Islington which all have their cheap parts as well as their more swanky sectors and are all good for amenities and transport links.
You might also want to think about the type of community you want to live in, for example, Kilburn and Cricklewood are very Irish whilst Golders Green is known for its Jewish community.
I am not sure how much a retail job would pay - not much - maybe £7 per hour (before tax). You would not be likely to get a work permit for that kind of job so presume you have something sorted out like British ancestry or student visas which allow you to do p/t work of that sort. Have a look at the section on visas and immigration for more info.
Hope this is helpful - feel free to ask away!
Cheers
Liz
