While practicing on an acoustic kit is every drummer's dream scenario, realistically it's often difficult to justify and control both the volume and space requirements of a full sized drum kit. In most cases, I'd steer people towards an acoustic kit with low-volume accessories instead of an electric kit as the playability and longevity is much better and upgrades can easily be made over time as you or your child become more serious about drumming.
However, this isn't always the best option for everyone. Electric kits are a great option for one main reason - the technology. Firstly, even entry level kits come with multiple sounds to fit different styles of music, so whereas low-volume kits require a little bit of imagination to 'hear' the full sound, an electric kit gives you professional sounds straight in to headphones or a speaker. Secondly, they all come with various practice aids only available with digital technology which can really help with timing and consistency.
Must-Haves
From the indirect experience I've had through my students, I've learnt that there's a few non-negotiables when buying an electric kit.
A Real Bass Drum Pedal
This is by far the most important thing to look for, as bass drum technique is often one of the toughest things for beginners so it pays to have the right tools to practice with. At the cheaper end, electric kits come with stand-alone pedals with a hidden trigger mechanism inside. Not only are these options prone to slipping around more, but the feel and triggering of these has been an issue for every single student I've taught with one of these set ups. Instead, make sure you buy a kit with a regular bass drum pedal which strikes a rubber trigger pad. If you can afford it, a kit with a real hi-hat stand is almost just important for playability. The first picture below shows what to avoid, with two stand-alone pedals, whereas the picture on the right shows a kit with regular hardware enabling much more successful practice.
A Mesh Snare Drum
At the entry level, most kits come with solid rubber pads, which not only lead to greater vibration through the floor, but don't feel nearly as realistic as a mesh head. Usually this upgraded feature will be shouted about on any manufacturer's promo, but is also easily spotted by the white head colour, rather than the black rubber of the cheaper pads. Further up the product ranges, you'll see the full array of drums with these mesh heads for an even better feel.
New(ish) technology
In the same way you'd never buy a computer older than 5 or 6 years, it's a good idea to avoid older second hand electric kits. Not only are companies constantly updating their technology to improve things, but over time the constant impact an e-kit endures can lead to triggering and hardware issues that can't always be fixed as easily as on an acoustic drum kit. This is less of an issue for higher RRP kits such as an old Roland TD-25, but I personally wouldn't recommend buying any kit with an RRP below £600 second hand as the lack of warranty and cheaper build quality means you'll rarely find good value for money second hand.
Recommended Kits
I've not had the chance to personally try out any recent electric kits on the market, so the recommendations below are based on the experiences of my students and some more general market research. Before buying any kit including the ones below, make sure you do your research, particularly looking for longer-term reviews of kits to see what other drummers' experiences have been.
Roland TD-07DMK
Roland have pretty consistently been the leaders in not just electric drum kits but in all digital instruments, so even their not-quite cheapest offerings are built to last with great features. This kit crucially comes with a real bass drum pedal, so technique can be worked on more effectively.
Yamaha DTX452K
Yamaha's electric kits benefit from using samples of their world-renowned acoustic drum kits, while their hardware is easily some of the best in the drum industry, so well worth a look at.
Final Tips
Perhaps even more so than with acoustic drums, really do go for the best kit you can afford. Unlike acoustic kits, upgrades and repairs are much trickier, especially at the entry level, and these cheaper kits really aren't built to last.
I'd really recommend sticking with either Roland or Yamaha kits. Alesis do make some good quality setups that are worth further research, but almost all of my students with their entry level 'Nitro Mesh' kit have had issues with it. Similarly, there's several beginner-only brands offering a lot more features for the money, but the components and sound libraries used on these kits don't come close to the quality of the two main brands.
If you're still unsure on the best kit to buy, the YouTube channel "65 Drums" is a great resource focussed purely on the digital drumming market, with constant updates on what's currently the best options for any budget.