I have wanted to get into the world of Speedrunning for a while now, but have never got around to do it, I mainly play games on my Switch, so I was wondering, what's the best way to record Switch footage for longer than 30 seconds or on games that don't support capturing? and what's the cheapest way to do so? Thanks in advance!

The cheapest way to do so is to simply point a camera like on your phone or a webcam at the TV (or at the Switch if using a Switch Lite). If you're using a Switch Lite, this is the only option you have because that is essentially a handheld console with no HDMI output.

If you're using a regular Switch, the best way is to get an HDMI capture card and use that to capture the footage of your Switch onto your computer where you can record/stream with OBS. HDMI capture cards can have a large range in terms of price (some you can get around $100, others upwards of $350) and you may need a decent HDMI splitter (or a capture card with an HDMI pass through) if you want to play off a TV while capturing the Switch. There are dozens of threads in this forum recommending HDMI capture cards, but it usually boils down to "what is your price range?"

I'd prefer a cheaper capture card, the cheaper the better, but I still want it to be good quality. I've heard of Elgato and Roxio being good quality, but I've never checked them out, thanks for the help!

i use the elgato hd60s, it was 100$ and it looks good enough

Elgato is a decent brand, but I've never heard of Roxio. Just be wary, whatever capture card you get, if it's a USB capture card, you're going to have some slight delay in the capture on your computer screen (could be upwards of a couple of seconds). This isn't a problem unless you're trying to play off the capture footage rather than a TV because, obviously, your inputs would be delayed and messed up by the delayed capture. In that scenario, you'd want to find a way to split the HDMI so you can play off an feed with no delay. Just something to keep in mind when searching for brands to buy (like I said, I would skim a few pages of this forum to find lots of posts/threads on this topic).

ive only heard bad things about elgato, a friend of mine had one and it barely worked he now uses it as a component to hdmi converter for his avermedia LGX2 which i recommend getting. i personally have the original avermedia LGX but its not manufactored anymore.

edit: oh yeah delay is basically nonexistant so if you really have to you can play off of the obs preview