Audacity, while free and useful, won’t be enough to do beat-oriented electronica. As mentioned, you will need a sequencer and some software instruments. The 80s and 90s have come and gone and there is no need whatsoever for hardware synths. At least not for a beginner.
However, some sort of hardware controller can be nice. For beginners, the Korg’s nano series is compact and affordable.
If you own a Mac, you can do surprisingly a lot with Garage Band. Grimes does all her music with it.
At $200, Logic Pro (also Mac only) is hardly free, but it’s a crazy, insane cheap for what you get. It’s far from easy to learn, but for $200 you get about $10,000 worth of excellent software instruments and plug-ins.
On Windows, for about the same price as Logic Pro, there is Cubase Elements, which comes with some good software instruments. (Again, maybe a bit pricey.)
A bit cheaper, around $70, there is Renoise. I have never used it, but it looks like a good software for what your son wants to do.
You’ll possibly need an audio interface. The built-in interfaces on many Windows computers suck to the point of being unusable for making music. There are a lot of choices, at every possible price point, but one possible option would be M-Audio products as they come bundled with Pro Tools. Pro Tools, for quite a while was to recording was Photoshop is to image editing, but its star has faded, and it has always been very poor at sequencing.
Other options:
Sonar X1 Essential at $70.
Acid Music Studio at $55.
If your son wants to use what popular electronica artists like Skrillex, Deadmau5 or Flying Lotus use, then Ableton Live it is. However, at $450 for the basic version, it’s definitely a bit steep! There is a basic version called “Live Intro” that sells for $100 that you might want to check out.