In AviSynth terminology, I think Lanczos3 is pretty similar to Spline36, and Lanczos4 is pretty similar to Spline64. It partly depends on whether you're upscaling or downscaling. Lanczos4 is often said to be better for upscaling, but introduces too much ringing for downscaling. Personally I think you can easily succumb to PPS (pixel peeping syndrome) with this stuff and start seeing differences that aren't really there. Even the less fancy "bicubic scaling with integration" that is used by Vegas (if "Full-resolution rendering quality" is set to "Best") is pretty close to those fancier methods. I use Spline36 in AviSynth for most stuff (if I bother going out to AviSynth), both upscaling and downscaling, and usually stick on a Vegas Sharpen FX later back in Vegas if I need to sharpen it more.
I know nothing about hyperbolic sine filter. As for speed, they should be similar. None of them are doing anything like motion adaptation so they don't need much juice in modern computer terms.
The ResampleHQ filter (here and here) for AviSynth was an attempt at gamma-aware resizing, which ought to be "better". I have tried it a few times and still use it sometimes, but it's really hard to percieve any difference over the standard resizers, at least in my footage.
Better than what? And not all Lanczos are equal. You have to consider the number of taps. 4 taps (Lanczos4) is sharper than 3 taps (Lanczos3), but introduces more ringing (halo effect).
p.s. I'm winging it a bit here from memory and haven't even read that page lol
I guess it's bilinear that should be avoided if anything. From the VP13 help about the Full-resolution rendering quality setting in the preferences:
Unless you have specific performance problems, choose Good. Choosing Best can dramatically increase rendering times.
Good uses bilinear scaling without integration, while Best uses bicubic scaling with integration. If you're using high-resolution stills (or video) that will be scaled down to the final output size, choosing Best can prevent artifacts.
I'm not sure what integration means in this context, but "Best" has served me very well for doing UHD>HD downscaling.