Selfhosted

Is he planning to also use the laptop as a laptop?

If not, there are small form factor PCs (especially if you're willing to buy used business stuff) that don't take up a lot of space that can be good options. Laptops have some features that are kind of nice on a server as well (the battery becomes a backup against power outages and you don't need to remote access or plug stuff in to use it because it has a built in display and keyboard), but I don't think they're so nice that it's usually worth buying a laptop just for that purpose. It's more a reason that repurposing an old one makes sense. If you're willing to pay the premium a new laptop adds, you can get some pretty low profile units.

with a $1000 budget they might want to consider building a computer as desktops usually provide better performance/per cost rather than buying a $1000 laptop

• desktop pcs can also be small if a small form-factor like ITX or mini-ITX is chosen (although mini-ITX can be pricey)

building is incredibly easy as there's a plethora of tutorial vids online and you're less likely to get screwed over by an Original Equipment Manufacturer (OEM) or retailer

• diy vs. buying a pre-built

the fediverse here also has an active community for support !buildapc@lemmy.world

Ideally he's needing something great for video encoding, and Linux friendly to boot.

What's the plan here, using the laptop for gaming and streaming, or only using the laptop as the streaming machine?

Is he doing transcoding on the hardware itself?

If so, despite their current shits-on-fire stuff, it's really hard to beat Intel QSV.

In any case, do not rely on AMD's VCE if you care at all about quality, because right now it's still awful.

QSV, nvenc, or do it on the CPU with x264/265.

(Not a specific laptop recommendation, but just a AMD-still-kinda-has-a-deficiency-here post.)

Go on Kijiji or whatever and look for a relatively recent used one with an Intel processor. It'll be a lot cheaper, and you don't need fancy hardware or features since you'll not be using it as a laptop.

You don't need a display. You don't need a battery. You don't need a keyboard or a track pad. You don't need a laptop. And you don't need to spend $1k.