Tip, budget for a clip on headstock tuner too (chromatic tuner, but I think they all are). Cheap ones are under 10 pounds, I've got this one
(or at least the one in the picture). You can get by without a case, even straps or picks, but a tuner is essential, especially if you're just starting.
Second hand is a good way to go, you do pay a bit of a premium for a new guitar. Though you probably do want to check you're not buying a really cheap one second hand. People say nice things about the Yamaha starter acoustics, but I've never tried one. I've got a Ibanez V50
, which is playable, though I did get a setup done on it. Also the extras aren't very good (fixed tuning microphone tuner, un-padded bag), except for the strap (it's a strap). Look for a company that actually makes instruments.