Definitely agree on the used idea. Ebay is full of used previous gen parts at great prices (stick with sellers with a deep history of 99% and higher feedback, avoid those with accounts less than a year old and/or single digit feedback. Avoid single digit sellers with suspiciously cheap prices for recent hardware like the plague - these are likely scammers.)
Personally, I’d avoid laptops if gaming is your primary interest. Performance does lag behind similar spec desktops, but more importantly, if something that isn’t ram or a storage drive breaks on a laptop, the whole machine is probably done. Not necessarily because the whole machine is unusable, but many if not most repair parts are model specific and can cost more than the laptop did.
Desktops can be repaired and upgraded per assembly, which makes them pretty kind to your wallet if gaming on a budget. I just scored an excellent condition 1080ti for around $150, and I know with absolute certainty that very robust off lease workstations from a few generations back can be had for $200-ish or less if you know what you’re looking for. Pair them with that 1080ti and you’ve got some decently capable hardware to play with!
I’ve got several gaming machines that I use to run everything from old stuff to heavily modded Skyrim VR and many new titles, and I pretty much only buy storage amd cables new. Everything else is purchased used on Ebay.
I have a shield connected to a projector through an av receiver. I love the setup for its audio visual fidelity, but I love the simplicity of operation almost as much. The shield remote turns everything on and off and handles all my streaming services + steam link flawlessly. Wonderful user experience.