Which shop?
I recommend PMT, Kristall Road

Guitars and amps
For blues and rock, get an electric guitar and amp, and/or a steel-strung acoustic. For jazz, it used to be the case that you had to use a hollow-bodied semi-acoustic guitar, but nowadays any style of guitar is fine - it depends what you want to sound like.

Epiphone make very good budget-priced semi-acoustic guitars.

As far as solid electic guitars go, I love the Stratocaster - it's so versatile, you can play any style of music on it. The American-made Fender Strats are lovely, but cost about £700. If you can't afford that the Mexican-made Strats (£350) and the Strats made in the Far East (£129+) are usually fine. I also like the Telecaster, and have one made by Vintage, costing only £200. Indeed, the whole of the Vintage range is excellent value for money if you are buying something in the lower price bracket.

I also love playing jazz on a classical nylon-strung guitar as this offers a large dynamic (quiet to loud) range.

If you are a beginner on a budget:
a decent nylon strung guitar will cost £90 - £150
a decent steel-strung acoustic will cost £120 - £150
a Fender Squier Strat will cost £129 - £180. I have a Yamaha Pacifica (£180) which is absolutely brilliant value for money.
a Marshall or Fender practice amp will cost about £130. The Park, Roland and Peavey practice amps are good too. But NB eventually you will want a better amp with a 12-inch speaker and probably costing at least £200, because the cheap practice amps are really just for geting you started - they tend to have a weaker, boxy sound.

More about amps:
If you want a valve amp for home use get a Fender Blues Junior (£400 approx): it's a one trick pony but with a classy blues sound. Get an overdrive pedal to go with it for lead sounds.

These days it's very hard to buy anything that is poor quality: simply get what you can afford. If you are looking for a small practice amp for home use, the Fender or Roland ranges are very good.

Metronome
This is a must, so you learn to play in time. They cost £17 - £30. Even better, get a drum machine and/or computor sequencing programme (Cubase etc).

Backing software
If you are serious about becoming an improviser you will benefit enormously from using a brilliant software programme called 'Band in a Box'. You can buy this from Jazzwise. (I think their website is called www.jazzwise.com)

Guitar tuner
This is not cheating! Get one. (£15 - £20). The Fender one and the Korg (CA-30) ones are good. Also get some pitch pipes (less than £5).

Music stand
Get one of these so you don't injure your neck or back.

Footstool
If you play acoustic guitar this is very useful for good posture: put it under your right foot. I have a lovely footstool made by a guy who has a stall at Leeds Farmers Market (every first Sunday of the month, Leeds Market). He is: H and B Kershaw, Stool Workshop, 17-19 Quarry lane, Woodkirk, Dewsbury, West Yorkshire, WF12 7JG, Tel: 01924 476 459 or 0788 432 7522. Ask for a number 27 stool, 7 1/2 inches high. Mine is in elm and cost £16.

Plectrum
Get a plectrum that is thick enough - 0.70mm for electric (for light strings ie .009'' to .042'') and 0.88 - 1.00mm for thinker strings, or acoustic guitar (which usually uses thicker strings).

A4 ring binder
Get organised.