To my experience, they won't supply any uniform at all except for a hi-viz vest to go over the top of whatever you wear.
Wear comfy clothes and shoes, trainers are ok but they'll probably get soaked through within moments on a rainy day - marching around in wet socks for hours will do your feet no good, so I had trainers for the dry days and my hiking boots for wet days.
Many turn up in jeans which are ok as far as dress code go but not great for delivery - usually get way too hot in warm weather and weigh a ton if they get wet. I had thin trousers, with waterproof leggings over the top if required.
Thin cotton t-shirt (not polyester or you'll be dripping sweat into your boots!), they don't care what colour (so long as there's no big advertising branding on it or offensive words, obviously!) because your hi-viz goes over the top anyway. You'll probably be surprised how hot you get even on the cold days so thin layers are better than a warm jumper.
Bring a decent waterproof for the wet days, you'll probably find it's better than the RM uniform 'stormproof' which leaks!
I think there's little to no chance of having a locker to store your stuff. I have all my gear in a small backpack which I keep by my frame in the morning, then stays in the back of the van with me during delivery - has lunchbox, drink, first aid stuff like plasters a must, spare pens, etc.
Fingerless gloves for the cold days, and a spare pair to change into halfway round the delivery when it's raining.
That's pretty much all that I turned up with, and I got uniform within six weeks then but they may have changed that nowadays (tho it's only 3 years ago!)
Welcome, I hope you enjoy it. Bear in mind that the first few weeks are likely to be the worst ones of your whole time here and many quit too soon in my opinion. Now that my body (and brain) has become accustomed to the RM workout every day I think it's a great job, and brilliant on a sunny day!