Yeah!
I love playing guitar, and I wish that everyone could enjoy it too!

It's not easy but it is really fun.
Ok, about type of guitar to start with... well, although I've been playing for quite a long time, I'm not so knowledgeable as I used to be, because I haven't read guitar magazines for quite a while.

(I really should start again... although all the reviews just taunt me with great-sounding guitars that I can't afford! >< lol) ...... So bear with me.
I recommend
not to get an Encore or Squier. They are the most common cheap 'beginner's' guitars, but I personally don't like 'em, and they have understandably a reputation for being exactly that - a cheap beginner's guitar. (I found the Encore to have a bit of an awkward fretboard somehow for me, rather chunky with high frets, and the Squier to be a tad heavy.)
There is no need to spend an absolute fortune, especially as you are just beginning and don't know yet how you will like it, but on the other hand, I suggest you don't get the very cheapest available, but rather, spend a little bit more and get something more 'middle of the range'. You should go into your local music store, explain yourself and ask to try some of their guitars within the price range you are looking for. You have to get one that you feel happy and comfortable with.
My guitar is a Westfield -
here is their website. Mine is in fact one of their cheapest! (It was bought for me as a surprise by my Dad, who also played guitar and knew what he was doing, and I paid him back later. ^^) I have almost no complaints about it; I can get a good range of sound out of it, and I particularly like the fretboard.

The only things I will say are that I have 3 single-coil pickups. Single-coil pickups are better for a clean, crisp tone; humbuckers (pickups with 2 coils) are better for a more... how to say it?... warm, full tone. Many guitars combine single-coil and double-coil pickups, so you can go for one that has the best tone for you.

Also, my guitar, being a cheaper one, I can't use the whammy bar on it very well without it going out of tune. That doesn't bother me; I just took it off and don't use it cos I don't really need it.
I also have to say that I don't use my Westfield for gigging, so I have no idea how well it would stand up to heavier use. However, I've spoken to a couple of people who have them, and they've all been complimentary about them, including 'my' guitar-repairer-man.
For a middle-of-the-range guitar I also recommend Yamaha. They're a good, well-established, sound make.

My acoustic guitar is a Yamaha, dating back to the early '60s, and I have to admit that it's superb. ::kisses fingertips:: ... but that's hardly a typical example, because it's an acoustic, and has had many years to 'wear in' and get its wonderful mellow sound.

But I have heard good stuff about Yamaha electric guitars too, and they don't all cost a fortune (in fact, if my Dad hadn't chipped in with the Westfield there was a Yamaha electric I was going to buy ^^).
Here's their UK page.
This is an American page and you're in Wales - but it's fun to browse around and dream! XD
Also, consider your amp. For an electric guitar, the amp is like half of the instrument! because it has a big effect on the final sound that comes out. For instance, although I have 3 single-coil pickups on my guitar, using my amp I can make it sound very fuzzy (lots of 'gain'), echoy ('reverb'), crunchy, twangy, mellow, or even as though I'm playing guitar underwater!

I get different effects by using a combination of different levels of gain (controlled via the amp) and different settings of tone (controlled by knobs on the guitar which dictate which pickups you are using). ^^
I'm not at all expert on amps, since I only have one!

My amp is tiny - a 10 watt 'practice amp', so-called because, well, you use them for practice only. They aren't powerful enough for playing gigs. However, a practice amp is all you need for starting off, when you're playing just in your house or garage. ^^ For instance, mine can create more volume than I would ever need in my house! >__<... XD. But it's important to get a decent amp, because a lot of practice amps (i.e. the small 10 watt amps) can have a really crappy, tinny, cheap 'n' nasty sound. >< Mine is a Park amp - they are made by Marshall - and I'm impressed by it. I can get a really good range of different sounds out of it, perfectly adequate for my personal practice at home, without it sounding 'cheap' or tinny at all. So I wouldn't hesitate to recommend the Park 10 watt amp to any beginner.
Marshall is a reputable make for amps, and
here is their home page.
Again, I can best suggest that you talk to the people in a music store and try out some of their guitars and amps to find out what you like the sound and feel of!

Also, you can read guitar magazines, which have reviews of guitars, amps and other equipment.
About the size of your hands...
it really doesn't matter!!! Seriously, do NOT be put off by thinking you have small hands. When you get to a more advanced level, sure, there are some things that are easier if you have bigger hands. But anyone with enough dexterity can learn to play guitar to a high standard without needing to have big hands/long fingers. As an example, I started learning (on a three-quarter sized acoustic) when I was around 4 years old, and moved to a full-sized acoustic at some point I can't remember >< but certainly before the age of 10, before my hands were fully-grown. Sure, my playing at that age wasn't exactly Steve Vai!

I just played a few chords. But you should be able to learn to play just fine. ^^ It's just necessary, to build up strength in your hands, which is hard at first but becomes easier with practice. Your fingertips will get harder, and your fingers will become stronger.
If you do have small hands, good technique is particularly important. Make sure to hold the guitar properly, and place your left hand correctly. A tutor or instruction books will be able to explain this!
Phew!

I hope some of that was helpful and not just nonsense to you...

Please feel free to ask any questions!