Here I list some of the things which, although not absolutely essential, I believe you need to get started on the guitar.  There are many opinions on which are the best, but my recommendations will certainly see you sorted with some equipment which will serve and last.  Some of this equipment is also discussed on the Tips n Tricks page.

Picks/Plectrums
If you play classical guitar you won’t use one, instead you may grow and shape your finger nails.  For strumming I would recommend a thinner pick, about 0.71 mm, and for picking something heavier, over 1.5mm, with a point.  Whether to use one, and which to use, is a personal choice.  If you are starting out, get a mixed selection off ebay so that you learn the shape and thickness you prefer.  This should only cost a few £s, whereas those in a guitar shop may be £1 or more each.  Brian May uses a coin – an old sixpence.  As with all things in popular music, there are so many variations that there is no right or wrong style, nor correct way to hold one.  Generally, the pick is held between the thumb and index finger and its use will take time to master.  There are claims that certain grips make it easier to play fast.  Get some help from a teacher or another guitarist when you begin and go from there.

Tuner
It’s essential that you develop the skill of tuning the strings of the guitar to each other by ear, but using a tuner will ensure that they are tuned to the correct pitch and accurately.  There are a number of types, but when you begin it doesn’t really matter which.  The ones which clip onto the headstock are very popular.  I think these can get lost and have used a small Korg tuner for years:  Korg GA Pocket Tuner (£11).

Capo
Attached to the neck of the guitar over the fretboard in different position and used to change the pitch of all of the strings.  You will have seen them, mainly used on acoustic guitars.  I still have my first one, which is a very inexpensive wrap-around type with a nylon strap.  I wouldn’t recommend these, unless you are really strapped for cash.  They have the advantage that they last for ever(!) and you can put it in your pocket.  The two I recommend are the Jim Dunlop Trigger Curved Capo (£15) and the G7th Performance Capo (£30).  With the Dunlop, you have to select the correct one for classical, acoustic or electric guitar.  There are many less-expensive copies, but I can’t say how durable they are.  They clamp onto the neck and you can’t adjust the tension, but they are used and trusted by professional guitarists.  They are sometimes left on the headstock when not in use.  The G7th is more expensive, but I like it since you can adjust the tension and it goes in my back pocket at a gig.

Music Stand
You don’t have to have one of these, but they are so useful.  Buy the right one and you'll only do so once.  Rather than craning you neck looking at music or chord sheets on a desk, a table, or your lap, you can sit with good posture using a proper music stand.  Do yourself a favour and don’t get one of the fold-away ‘frame’ style.  I suppose they have the advantage that you can carry them in your gig-bag, but they just don’t last and get as ‘bent-out-of-shape’ as you will as you try to straighten them out and assemble them.  Save up for a more durable one similar to the JHS On-stage Perforated Music Stand (£40), which will last for ever.

Gig bag
Your guitar may have come with a gig-bag and they’re really useful.  Even the budget ones will give some protection and they generally have carrying straps and pockets in which you can put your other paraphernalia.  I can’t recommend any in particular - the ones I’ve bought have all fallen apart in time.  (Or caught fire - which is another story!).  I suppose the best are the Mono brand, but I haven’t been able to justify the expense yet.  If you have a guitar with an angled head-stock (Gibson, Epiphone, Gretsch…) you’ll need a pretty sturdy gig-bag.  

Guitar stand
At home, keep your guitar on a stand in a place where you always have access to it.  You won’t believe how much more you will pick it up and play.  Even the small task of opening a case or un-zipping a gig-bag can be enough to put you off.  It will also save the guitar from being knocked over and damaged.  They can be really inexpensive - I use small fold-up ones which I can easily transport and use at gigs as well as at home.

Strap
Essential if you’re going to play standing up and some use them sitting down as well.  Thousands to choose from, so you’ll find one you like.  Personally, I prefer fabric or leather as I find that the nylon ones slip if the guitar is top-heavy.  If your acoustic guitar only has one strap pin, you’ll need the type which can tie around the headstock.  Straps can be really inexpensive, or even free with strings.  If you’re a student of mine I have loads and can let you have one to get you started.  They come in different lengths.  If you are large, or tie the strap to the headstock, you’ll need a longer strap.

Unless the strap is extremely stiff, you’ll need some sort of strap-lock, or your guitar may suddenly free itself and plummet, expensively, to the floor.  I like the little plastic ones, but these don’t allow the strap to be easily removed.  What is really cool is to use the red plastic washers from bottles of Grolsch beer!

Finger Nails
Free, if you use your own.  :  )  Not essential, but classical guitarists and finger pickers often grow and shape their nails.  If you have weak nails, as I do, you’ll find they break easily with steel strings, unless you keep them to about 2mm in length.  Many go to the nail bar and have gels or acrylics.  Yes, really.  The tone is different to that of your own nails, but they’re very durable.  You only need your thumb and three fingers done on your picking hand and to have them re-done every three weeks.  If you change your mind, it takes quite a few months for your own nails to recover, during which time they’ll keep breaking even when you put your socks on in the morning.  Mark Knopfler famously plays finger-style and doesn’t grow his nails.