Bread, milk, eggs, butter and cheese in the fridge. Pasta, rice, flour, sugar, dried lentils (I buy bags of mixed called soup mix). Packet sauces (white sauce, casserole mix etc). Tins of beans, soup, peas, other veg and tinned fruit that you like, jam. Coffee and tea.
If you don't 'cook' then get jars of sauces - pasta sc, sweet and sour, curry etc. If you do then you will need oxo, tomato puree, garlic, herbs and spices, worcster sauce, soy sauce etc.
There are lots of threads in the food and credit crunch sections on here about meal planning and budgeting so you should check them out. I shop online, apart from being convienient I find I spend less as I get what I need rather than being tempted along the way.
You will need basic household supplies, tool kit, light bulbs, shoe polish etc, basic cleaning equipment (hoover, mop and bucket, cloths, washing up liquid, bleach, window cleaner, and washing powder).
As for budgeting you need to keep an eye on things. Say you get paid on the 1st then you want all your direct debits to come out then, rent, council tax, insurances, gas, electric and water.
Then you see what is left. Prioritise the rest of your money. How much do you need for the food shop, petrol or bus fare any other expenses that you need. After that you have your 'spends'. IMO you want to be saving as much as you can. Once you have your own home there is always something unexpected that you have to pay for - washing machine might break, car needs new tyres, boiler packs in etc. Even if you are in rented and LL would pay for major jobs there will still be something. So save as much as you can.
The rest is yours to play with!! You will have to be frugal - don't buy magazines and sweets when you get petrol. Don't get a coffee on the way to work, take a packed lunch etc. All of these small spands add up to a lot in a month and a lot of people don't realise what they spend. If you get a coffee every day at work at about £3 then thats £15 a week, £60 a month, £720 a year!!
I'm sure I will think of more but I have to go and put DD to bed!, I'll be back 