It's really difficult to just suggest one thing, or even a couple of things to look at. I've spent a lot of time evaluating the various scaling options in madVR as they have evolved over time.
If your system can handle it, I would recommend simply using Jinc 3 with the anti-ringing filter enabled, but not the linear light option, for both Chroma and Luma upscaling. Never use linear light for upscaling.
Catmull-Rom with both the anti-ringing and linear light options enabled seems to give the best quality downsampling - this is the only option where linear light scaling is acceptable.
If your system can't handle that, or you are primarily watching a lot of highly compressed, low resolution videos, then things get a bit more complicated.
After Jinc 3 AR, my preference for Luma upscaling is SoftCubic 80. (without linear light/ar) As the name suggests, this gives a soft result, but it avoids introducing any ringing artifacts, tends to avoid aliasing very well, and can de-emphasise mosquito noise in poorly compressed content. (older DVDs for example) In fact, once we get per-resolution scaling options, I am likely to switch back to this for SD upscaling rather than using Jinc 3 AR. I watch a mixture of HD and SD content though, and Jinc 3 AR looks better with the HD stuff.
If that is too soft for you, you may want to try Lanczos 3 AR which gives similar results to Jinc but with more aliasing, and less of a performance hit, or Mitchell-Netravali which is in-between Lanczos and SoftCubic for sharpness, and performs very well. Both have a tendency to show aliasing and ringing though.
With animated content, I would definitely be leaning towards the softer scaling algorithms.
If you need to reduce Chroma scaling settings, I would try Lanczos 3 AR, then Bicubic 75 AR if your system can't handle that. Chroma scaling is quite well optimized these days though, so most systems should be able to handle Jinc 3 AR.
If you are having performance issues with downscaling, the first thing to try is disabling linear light scaling with Catmull-Rom. (turn that off before the anti-ringing filter)