If your situation allows it, an acoustic drum kit is by far the best option to go for for the following main reasons;
Best Playability
Put simply, electric kits are built to imitate the sound and feel of an acoustic kit, but in reality they never get close enough.
Easily Upgraded
Drum Kit's can easily be purchased as all-in-one packages, but these can easily be added to or altered over time with the addition of extra cymbals, better quality snare drums and brand new drum heads
Strongest 'Investment'
Sadly only the rarest of vintage drum kits might even come close to gaining in value, but a good quality acoustic kit will certainly hold it's value considerably more than any electric kit
What To Look For
Not all drum kits are made equal, so here's the main things to look out for;
Buy From a 'Proper' Drum Brand
A good rule of thumb would be to only buy a kit from a company that also makes top-of-the-range kits. These brands want to make a lasting impression on you so that you'll remember them years later when your budget may be much bigger, so their entry level kits are great quality.
Check The Sizes
Bass drums in particular can get quite big, so for young children look for kits with an 18" or 20" bass drum, as any taller will force the Tom-Toms to be set up too high.
At the same time, unless you're buying for a very young child (5 or 6), I'd avoid 'micro' kits such as the Ludwig Breakbeats kit, unless you're really keen as these tend not to be so versatile.
If you wanted your child to learn music grades, make sure the kit you buy is a "5 piece", so has a Bass Drum, Snare Drum, 2 Tom-Toms and a Floor Tom, as some kits only have one Tom Tom.
Check What's Included
Somewhat confusingly, the more you spend on a drum kit the less you get...
Kits priced at an entry level will almost always include everything you'll need, but once you move further up in budget, it's assumed by drum companies that you'll have your own preference over cymbals and even drum hardware and pedals, so make sure you check carefully! If you're buying from a dedicated drum store they'll happily make sure you go home with everything you need.
New or Second Hand
Drummers are always swapping out their kits for something different, so drum stores and eBay/Facebook Marketplace are full of second hand gear. So long as a kit has been well looked after, aside from the initial drop in value when purchased brand new, a second hand kit after a couple of years should pretty much stay stable in value. The main thing to look out for if you're going to buy a used drum kit is the hardware, which refers to any of the metalwork attached to the drum or any of the stands, as these can wear out or rust over time.
The main advantages for buying brand new, aside from the excitement of it(!), is that the hardware will be super reliable and there's no chance of hidden damage to the drum shells which could affect tuning.
If you're unsure quite what to look for with a second hand kit, I'd definitely recommend searching in dedicated drum stores rather than eBay or Facebook Marketplace.
Some Recommendations
The drum industry has come on massively in the last decade or so, with nearly all major manufacturers offering great beginner drum kits. I've listed some options here;
Best Buy - Yamaha Rydeen
Yamaha are one of the most respected drum companies as far as build quality, especially with their hardware. With entry-level kits, this definitely shouldn't be taken for granted as so many non-branded kits really fall short in this aspect.
This particular package comes with a great full hardware set that should last years, as well as a great entry-level cymbal pack.
Other Great Options
Gretsch Catalina
Tama Rhythm Mate
Pearl Roadshow
Final Advice
As I mentioned on the main Buying Guide, you definitely get what you pay for. There's absolutely hundreds of entry-level options available, but unless you're buying for a very young child below 6 or 7, it's not worth looking below £500. Cheaper than that and the quality falls through the floor, the kit will be falling apart within a year or so, and in case you or your child no longer want to learn, it won't have held it's value much at all.
Buying second hand is hugely recommended if you're on a tighter budget, and remember you can always upgrade different parts of the kit over time as your budget and interest in the drums increases.
Once you've got your acoustic drum kit, you may find you need to control the noise a little, so click here to read my advice on the best low-volume options available to you.