So you are looking at about £1900 after tax, NI, 4% pension and student loan.
£333 into a LISA each month (Skipton do one) as if you save that each year it's £4k and the government gives you £1k. You can only use this for a 1st house purchase up to £450k or for your pension - if you access it before you will pay penalties. I wish I'd started doing this earlier. Standing order on pay day.
Then accessibly savings - for holidays, but also for bigger purchases e.g. deposit for a flat. Any high street ISA is much of a muchness interest rate wise. Suggest £300-400 a month, but also put a sweep on your account to take anything on the day before payday into your savings. Standing order on pay day.
I'd also up your pension to whatever your grad scheme match as a minimum. So if they offer 5% contributions, you should put in 5% too. You should put in more - it would be wise but I understand you don't want to go into full on savings mode right now. Cumulative interest goes along way though, and your next job pension might not be as good.
So you've still got about £1000 left over. Depending on where you are, you could be looking at £400-800 rent for a room, plus bills (council tax, broadband, water, gas/elec) of about £100 contribution (shared house). Until you move out I would consider putting what you would pay on rent (or at least 50% of it) into a specific savings account for rent and deposit. Standing order on pay day.
Travel could be free or it could be a car - can't estimate.
Fun money - important as it keeps you going. I give myself £50 to buy any coffees or meals out, going out, hair cuts, clothes etc. £200 a month to spend how I like. If you're going out regularly, this won't go far. I choose my social life a bit more sparingly now e.g. I'd rather go for one really nice meal to a restaurant I've been wanting to go, than lots of cheaper pub lunches or things. You could make it easy on yourself, transfer this to a Monzo card away from your main salary account and then a) you don't spend more than you think and b) you can easily see how quickly and where your money goes.
Food - make your own lunches so your fun money goes further. Don't buy coffees out - get a keep cup, buy yourself a french press and enjoy better coffee for less.
Reconsider expenses such as gyms, high cost phone contracts etc - it's much cheaper on your income to buy a phone outright and then pay a £10 a month deal.
Once you have your standing orders in place, it's so much easier because you know what you have left.
So thats:
- a LISA
- an instant access savings for holidays
- an instant access savings for rent/future deposit
- a monzo card for fun spending money
Before I went into full savings mode, I wasted my money on picking up bar tabs, being very generous and paying restaurant bills, eating lots of (in hindsight) mediocre meals out, and not planning in advance for big purchases eg holidays just made them so much more pricey. Since being more aware I've gone on trips all over the world, and I've got about 70% of the way towards a sizeable house deposit. I much prefer living this way.