Congratulations on the job Ross and welcome to the commuting club. I'd pretty much echo everything above. You'll soon find out (the hard way!) if you need warmer gloves etc. I'd recommend getting a buff. It's a fairly cheap and handy piece of gear that can be used to keep various parts of your face and/ or head warm, can be stuffed in a pocket etc. And you can also start collecting them and then proudly announce you've got more and better buffs than Anth and myself.
As for waterproof trousers I think they are love or loathe but you will find out. Personally I've never found the need for them, but it's personal preference. My attitude is that you're going to get wet no matter what and a decent set of tights will keep the worst of the water out and act like a wetsuit to keep you warm-ish.
As for how to carry your gear, start with a rucsac if you've already got one (minimum outlay). If you find out you don't like it, it's causing sweaty back syndrome or - as I find - restricting the movement of your head to look behind - you can consider panniers or a courier-style bag. I use both, depending on how much I have to carry to work on any given day.
Both are made from waterproof material, I never saw the point in buying non-waterproof ones only to have to then buy and fit waterproof covers that you have to remove to get into the things. The covers also can't cover the whole thing - straps and clips have to poke out - so water will always find its way in.
There's a lot to be said for vests. Merino if you're up for the investment, you'll find them warmer if they get damp and they'll (you can get a good icebreaker one for 50 bucks, great for all sorts of activities) feel nicer on your skin and they'll go a LOT further inbetween washes (so you'll need to buy fewer).
Always carry spare batteries.
I highly recommend not buying the cheapest pump around. I'm a bit of a salesman for Lezyne Road Drive pumps. If you need to rely on a pump to easily get a tyre up past 100 PSI and to be able to work the thing with freezing cold hands, in the rain and not have to hold the adapter onto the valve, and not have it rip the neck off the valve, then it's well worth the £30. Everyone that I've let play with it is heartily impressed and I find myself jumping to the front of the queue to help with a cry of "I'll pump" when there's a puncture on an ERC run.
Oh, and always stop to check if a cyclist in mechanical distress is OK and needs any help :)