Real-time video encoding is computationally demanding... opposite of budget friendly, in general.
However, old H.264 encoding can be offloaded to dedicated, efficient chips (ex NVENC GPUs, etc) which helps.
Any non-bottom end and/or thin and light should be capable... assuming decently configured Operating System (stupid, excess background processes and OS eye-candy disabled) ... but, it depends.
1. Using OBS Studio to record YouTube videos is like using a battletank as a fly swatter... complete overkill, not a good fit, overly complex, etc. I really enjoy OBS Studio, but recording YouTube videos is NOT a good use case, imho
... and other basic screen recording.
Have you looked into the Operating System's native Recorder? there are other much lighter-weight (system resource demanding) tools out there for simple screen recording
That said, things I'd recommend to consider before making a purchase
- how long do you want this system to last? laptops have very limited (to none, depending on model) upgradeability, so 'choose wisely'
- If you are Recording, do you plan to use those Recordings as is? or do you plan to edit them? if edit, then look into your Video editor requirements (ex DaVinci Resolve's VRAM requirements for 4K video).
- Are you planning to livestream? if yes, current standard is H.264, but is likely to change in next couple of years to AV1... budget-friendly (depending on how you define that) and AV1 don't go together well at the moment. Keeping CPU free for other work, and GPU-encoding AV1 offloading real-time video rendering takes a new, powerful discrete GPU.
Intel ARC and AMD GPUs are improving relative to livestream performance and reliability, but if you want low-effort, low drama, it just works well, and you want 4K support then you are probably best suited to get a system with a discrete nVidia GPU with NVENC (beware some lowest end models and specific NVENC capabilities (or absence thereof). There are many threads of AMD and Intel GPUs driver issues... ymmv
Buying a laptop now that doesn't supporting Windows 11 is hard to do... even though I'm personally avoiding Win11 while I can (typical every other Desktop OS release from MS last 2.5 decades, complete junk).
16GB RAM at least. Depends on other laptop uses as to whether to get more
I like a decently long lifecycle (hard to do with a laptop, regardless), so I avoid the equivalent of intel i5 or lower CPUs.
beware cheap DRAM-less SSDs (and their low sustained write performance, which you need for video recording.. probably non issue at 1080p, but 4K?)
a gaming laptop (no need for top-end, expensive models) will probably work fine, but so will plenty of others... problem with a recommendation... is that there are so many other variables to consider than what you've described