Thanks everyone so far! While I'm not planning, at least for now, to make such a channel myself. If I had the experience of some here, perhaps (not that beginners can't have their own channels, perhaps discussing their learning process and their ways of grasping things as they go). I did however think that the answers you provide could be useful to anyone that does take this on, and the more supportive/informative tips we can accumulate, the more new interesting channels we may end up seeing.
Video editing:As was mentioned, I myself would recommend not going with expensive software if the channel is for fun (if profit is immediately the plan, perhaps expensive software may be a decent long term investment, but there's probably little reason to begin and 'feel the waters' using such things).
YouTube has an editor for example which might be enough to do most of the basic operations necessary. This thread is about YouTube, but if someone e.g. wanted to use Vimeo or another similar website, they might not have one included (I haven't used them to create content, so I'm not sure).
In either case, I would start first with free editors for simple editing.
E.g. Virtual Dub, Avi Demux (both for cutting/joining segments, simple filtering), and Fusion. Handbrake for conversions if necessary. Fusion not open source, but is a really powerful piece of software (professional level), and the free version comes with some limitations, most of which wouldn't matter for simple video editing (adjusting colors, adding text, animating things, so forth - it supports loading 3D models too). More and more free and/or open source video editing tools keep popping up. It's important to find one that seems
simple to use for you, or at least simple enough that you feel you will be able to learn it as you go along.
If on Linux, it has a lot of awesome video editors of its own.
As for fancy editing, I haven't noticed that many electronics channels use too much fancy editing (probably mostly standard cutting/joining segments, adjusting colors and contrast if needed and maybe removing audio noise - which Audacity can do decently - and such). Even Dave himself mentioned something related:
5. Don't fuss over details or try to "polish" your video. If it takes too long to make videos then it will become a chore and you'll give up easily.
It could apply to video editing. If you spend 99% of the time on video editing, it probably won't be fun to do. Unless you are interested in video editing specifically. For example, 3D animations can be used to make instructional videos. These have a lot of designing, rendering, editing, and perhaps no camera filming involved at all.
Camera/recording:As for Hardware used, from what I understand BigClive used a tablet and a smartphone or two (and maybe something else?). There are no quality issues with his videos what-so-ever. So, unless you want to record at 1000 FPS (I think there's a phone for that too - but might be pricey?) or want some special macro/zoom features, you probably don't need to buy any recording equipment. You may or may not want to buy an external microphone if it works with your phone (first try, maybe it sounds great already). If you need one - I would search for a cheap solution if you're willing to wait until it arrives - they can give impressive results for the price. If you're recording voice overs on PC, if using an integrated soundcard, you may experience some unwanted noise. In that case, I would consider getting a cheap (or as desired) USB Microphone, even the cheapest should still be able to remove some of that noise (unless you have very low noise on your recordings already, some high end motherboards might have decent sound-cards).
PC hardware:Most likely, you won't need a "beast of a PC" to do video editing and what you have might be completely fine. If it's taking extremely long (or you're processing high resolution, high FPS content), then perhaps there's some way to make the workload lighter using different filters/settings or use faster software.