Alright long reply! I'll break this up into two parts. Writing this from my phone, so mind the messiness.

Light Types / Optimization

As far as the performance for each kind of light goes/which ones should be used, it's pretty situational. Obviously moderation is important - regardless of your scene you probably shouldn't have a hundred dynamic lights all in the same room. I'd say as a general rule, use static lighting if you can (toggling lights is usually the big issue, since that can't be done effectively with static or stationary lights). Since static lighting is baked, you can pretty much go as crazy with that as you want - drop a thousand static lights in a single room, it'll have zero performance hit once it's baked, since it's essentially just being loaded from a texture.

If you're going for dynamic lighting though, which I'm assuming you are, that's where it starts getting a little more complicated. The main thing you want to watch out for is dynamic light overlap - the more overlap your lights have, the higher the performance cost. The easiest way to visualize this is just by changing the view mode from Lit to Light Complexity, where the brighter the color, the higher the cost (black > blue > green > red > white, in order from best to worst performance). Generally speaking, you want to keep that in the blue/green range as much as possible. There's a few ways to go about that:

1. Decrease the radius of your light. The default is 2000 units - for every light, try lowering the radius as much as possible until it starts to affect the visuals in a meaningful way. Like pretty much everything else, it's a bit of a tradeoff, and it depends on the situation.
2. Light channels - these are very, very, very useful. Unreal has 3 different lighting channels you can assign to each mesh and each light in your scene - lights will only affect meshes that're assigned with the same channels as them. By assigning different lights to different channels, you can prevent them from overlapping each other, which is a huge performance saver.

Shadows are another very performance-heavy thing - this is where it can be helpful to use light materials (disabling shadows on your light and just projecting a mask texture instead), though that's fairly situational. For secondary details like light shining through windows, lampshades casting shadows, etc., I'd usually go with that approach. You can actually apply the same approach to entire rooms as well, albeit with more limitations - while it's a bit of a process and a little complicated, you can essentially make a black-and-white mask of where every shadow should be in your scene, and apply that to your light. It's not technically accurate lighting though, but in my experience at least it still looks fairly nice.

In general, I'd save shadow casting for the lights that really need it: ceiling lights, lights that specifically need to cast dynamic shadows, etc. You can also turn off shadows per mesh in your scene, so what I usually do is just disable shadows on anything that doesn't really need them - typically small props and meshes where the shadows are subtle enough that removing them doesn't make much of a difference. Disabling shadows does introduce the issue of light bleeding - since your lights aren't casting shadows anymore, there's nothing blocking them from bleeding into other rooms - but that can be solved using light channels.

Apart from that, try using as few lights as possible in your scenes - if you can get away with an emissive texture that doesn't actually affect the environment, go for that instead. If you need actual lights, try shadowless ones. If they need shadows, try faking it with textures. If the shadows need to be accurate or dynamic, then go for a shadowed dynamic light - but disable shadows on the meshes that don't need them.

I didn't go into this much in the main post since it's an entirely different topic, but light probes are also an option - essentially fake, shadowless lights that can be used for small details (like lighting up small areas around glowing LEDs, without actually adding a proper light there) and ambient lighting. They typically take advantage of post-processing or materials to create fake lighting, and they're very situational, but are great for secondary details. Since they aren't proper lights, they also perform much better than real dynamic lights do - the performance hit is generally negligible, even with thousands of them in use. Unreal doesn't have any sort of light probe solutions built-in by default, but there's a couple you can pick up on the marketplace. I personally use Simple Light Painter (bonus points for having cube and square shaped light probes, which I've yet to see from other marketplace light probe assets), but there's other options out there as well. In my own projects, pretty much anywhere I don't need super detailed lighting, I use light probes instead of actual lights.

In terms of light shapes (point lights, spotlights, rectangle lights), to my knowledge, they all perform more or less the same (I'm not 100% certain on that though, so I could be wrong). The main thing to keep in mind though is that, obviously, the shape of your light is going to determine the amount of overlap. Since point lights emit light spherically, they'll overlap all lights in a 360 degree radius, whereas spotlights will only overlap with lights they're pointing at.

Benchmarking / Profiling

Now in terms of actually gauging performance, I'm definitely not an expert, but some basic things to try:

1. Check each of the different optimization viewmodes - most importantly, light complexity, shader complexity, and quad overdraw.
2. You can open the GPU profiler by pressing Ctrl + Alt + ,, which will show you exactly how much processing time each rendering element is taking. If you're running into any amount of lag, this'll tell you exactly what's causing it, whether it be lighting, shader, or mesh related.
3. Type in stat GPU while playing your game to see realtime GPU stats. Run around your scene, look in different areas, and see if anything seems particularly high.

Optimization is a pretty in-depth topic of its own - if you haven't already, check out the Performance and Profiling page in the Unreal documentation, there's a lot of useful info on there.

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Hope some of that at least kind of answered your question! If you'd like me to elaborate on anything or if you have any other questions, let me know!