Make a list of all your favourite vegetables, and then look them up to see how easy they are to grow. Also, make a list of any you and your household really hate, and don't plant them under any circumstances!
T&M sent me a nice voucher when I emailed for a catalogue a couple of weeks ago, as did Brown's. Alternatively, try places like Wilko (I think they're doing 3 for 2 at the moment) or Lidl for cheap seed. Simply turning up at the allotment site on a Saturday and looking enthusiastic (if you can bring a jug of homebrew, that'll help) might be good for a few plants from people who've oversown. If you know anyone near Didcot, I'm up to my eyeballs in chilli plants at the moment, and probably other things later in the month.
I'm surprised no-one has mentioned Joy Larkom as a good basic book (something like "grow your own vegetables"). Plus that great favourite - whatever's in the library, or cheap in a charity shop.
Get a good spade and fork - wave them around a bit in the shop to make sure they balance nicely and are the right size for you (if you're short, get a short handle; if you're tall, tear your hair out and wreck your back, because IIRC my mother who's only 6'1" had to make her own handle to fit her). Same for a rake (get the sort with fairly short teeth, not the springy sort for raking leaves up) - if it's too heavy at the head it's very unwieldy to use, although you can add a counterweight at the butt end to help.
I'd suggest you get half-trays or modules to sow seed in, as full-sized pans are too big for most things. Plus you'll want some gravel trays to keep your window sills clean. Alternatively, start saving plastic punnets and tubs from the supermarket (hummous tubs are a good size for things you only want a few of).
A trowel is very useful, and a hand fork is pretty handy too (they often come as a set) for planting things and for digging out individual weeds. Try to scrounge up a few bits of wood to make dibbers (pointy sticks for prodding planting holes). One the size of a broom handle is right for leeks and brassicas, and a small, pencil sized, one for seeds and small seedlings. You can use dry branches or anything really, and sharpen them with a stanley knife. If you're bored on a rainy day, you can make them neat with sandpapered ends and lathe-turned handles, but any old stick with a rough point sharpened will do the job.
Watering can: make sure it's one you can lift comfortably! If it's a long way from your plot to the standpipe, have one for each hand (or a bucket that you refill from) to save you journeys.
Scrounge or buy some timber for a compost bin. Four good uprights (fence-post sized) and some planks or boards. Plus some preservative. There's often timber on freecycle. As a stop-gap, a cardboard packing crate is better than nothing, and will buy you a month or two before it rots.