When learning any instrument you have to consider what you need, to learn to play. In terms of learning to play the drums there are lots of options, but I will focus on my general advice which is always about getting what you need!
Acoustic V Electronic
Electronic Kits - Pro's
Electronic kits are exceptionally good these days and, in terms of practising, it is not much of a contest between electronic and acoustic when you are learning to play the drums. The main problem with learning to play the drums is the noise. Electronic kits are simply a much more realistic option as you can control volume with an electronic kit; down to almost silence.
Electronic kits are: compact, portable and, when used with headphones, allow you to easily mix playing-along with songs from your laptop, tablet, or, 'phone seamlessly and silently. Unless you have a very large house with no neighbours the electronic option wins every time. If you live in a flat or have a smallish corner of a bedroom, then electronic is the only way. Drum kits are not huge, in themselves, but they are deep from the front of the bass drum to the back of your drum stool, so it is often about how far they come out into your room to be able to sit comfortably behind them.
NOTE: This is not a perfect sitting position, but does show how much depth is required when you are playing a full size acoustic bass drum..
The snare drum and floor tom should be closer together and more in front of you. The model sat here should be facing forward and not off at a position that is at 10 o'clock. the cymbals should be more symmetrical so movement to the left and right is even.
There are lots of benefits to electronic kits.
Always sound good
They do not go out of tune
Range of different drum kit sounds
Record into your computer (USB/MIDI) so great with interactive learning software like Gigajam's Xtractor
Headphones for near silent practice and simple audio connections and mix from your audio player, laptop, phone or tablet
Portable and lightweigh
There are a plethora of electronic kits on the market and very hard to compare each one like for like, as they have very different features. Second hand kits, you can get for about £200. Brand new you do not need to spend more than £500.
I would always recommend the Yamaha DTX430/450 as they come with a 'proper' bass drum pedal. This is the only purist element I would look to insist upon. As a drummer you really need to get the feel of how a beater plays a drum head, as well as learn to feel the spring in the bass drum plate, so you can work with it when playing foot and leg strokes.
Acoustic kits - Pro's
If you are going to play live with other musicians then it is going to be an acoustic kit; so a serious drummer of any experience will probably need both - but I would start with an electronic kit.
Acoustic kits start to become more of an essential when you are moving into any type of live work and the real feel and, in all honesty, the control of volume, is a skill that has to be developed through technique and experience; developing the touch of the instrument comes with time. Drums are loud by their nature, so developing the touch to control the instrument so you can play at both quiet and loud volumes, as well as everything in-between is a skill of its own. Nothing worse than a drummer trying to play quietly and sounding inhibited and uncontrolled, you will have to learn to work with the instrument and control your technique so you can play truly dynamically. You will not really learn that on an electronic kit of any description or price.
Acoustic drums also have lots of different sounds within one drum, as do cymbals, so learning how and where to hit the drum/cymbal and with which part of the stick can only be fully developed once you have moved onto an acoustic kit. The variables of sound are enormous on an acoustic kit and experimenting with using different parts of the stick, playing in different areas of the drum and on your cymbals is the bit that cannot be replicated with any genuine sense on an electronic kit, again however expensive it is and whatever it says in their literature.
A decent and sensible starting acoustic kit is going to be between £600-700. That will get you a good well made kit that will sound reasonable and have some genuine durability, which is an issue overlooked too often, but really important, as this is something that is going to be struck regularly!
Kits can come with a starter cymbal pack such as the one pictured below. It is Pearl Export with Zyldjian cymbals.
The Export kit will last forever ( well, a long time), and can be used as a decent semi professional kit, so you will get enormous use from it. In time you will want to replace the starter cymbals. Cymbals are ferociously expensive, relatively, but good ones sound brilliant and average ones are like tin pots. This is an inescapable truth I am afraid. Get used to the idea that cymbals will cost as much as good drums as you develop your ear for sound.
Purely for information, at this stage, I personally use Sabian AAX and HHX cymbals and for indicative purposes see here
Makes and Models
Yamaha for electronic kits
For electronic kits I favour Yamaha as a brand over its rivals. Roland make utterly fabulous gear, but more expensive and I am not sure that they offer better value or outcomes for the learner. Professionals may well take issue over the high end pro kits as they are often the weapon of choice, but they are wonderfully expensive and that is not where the overwhelming majority of you will be coming from.
Yamaha tend to come with more usable features for the beginner and semi pro - like connectivity and are less expensive. They come with the proper bass drum pedal at lower price points and they do not use the mesh heads which for me are a poor replication of real drum feel. For a real drum feel you need to play - a real drum.
Personally, mesh heads are like playing on a tennis racket for me. Other drummers will have a different view and that is fine. The rubber heads now employed are much less harsh on your wrists than the early incarnations were and with appropriate technique provide a very good and reasonable replication of playing real drums.
You always have to play electronic kits like they are electronic, because you are triggering samples and not generating the sound by the way you hit the drum. There is an adaptation to your technique and you should be aware of that as a player. There may be times when you will need to play both electronic equipment and acoustic side by side, especially in modern music, so you need to develop the right techniques to play both and either. It is not about hitting. It is about playing suitable strokes to get the sound you want from whatever it is you are playing. That in itself is not an electronic v acoustic issue, that is drumming in general.
Pearl Drums and Sabian Cymbals
Purely a personal preference in these as there are so many fabulous drum manufacturers and cymbal makers. For a start, the Pearl Export model has been the best beginner kit since time began. That remains. It is not a beginner kit like other manufacturers, it is a good decent solid reliable 10 years out of this kit. It has always punched above its weight. For cymbals there are three major brands, Paiste, Zyldjian and Sabian. For me all the others are also-ran's, although there are indeed other choices that you can explore. For simple reliability I would recommend the major three without hesitation. Be mindful, the entry cymbals are just that. You genuinely have to spend decent money to get a great cymbal sound. There is no way around that and I have had to build up my cymbals bit by bit because of the cost.
In truth. after speaking with parents and learners alike,the most common piece of advice I give people is go on Ebay, Gumtree, Shpock, find a DTX 430 or 450 second hand for sub £300. If you want to play in a band get a second hand Pearl Export with at least a ride, crash and hi hats. When you move up the ladder to better gear, you will get most of your money back and have had good use.