"from my understanding a chinois strainer is much more expensive then a china cap but much more finer which is needed for stocks"
That is correct. A Chinois and a China cap are not the same piece of equipment. The only similarity is shape. A China cap is typically made from solid SS and is drilled so in essence it's a SS cone shaped colander.
A Chinois is also usually made from SS but has a band of solid SS around the opening and the cone is made from a fine SS mesh.
I agree with FP on Coffee filter use.... S L O W. I suspect most of us are talking about coffee urn filters due to the size. The other issue with coffee filters is that they are totally impractical for any thing that you might need to press through a fine screen. You won't be making raspberry sauce by pressing it though a coffee filter. The other problem with a coffee filter is they cog easyily which can be a RPITA depending on what you are doing.
For home use you can get small fine mesh strainers at any kitchen supply. Sur la Table and Williams Sonoma will have them. The diffence between a mesh strainer and a chinois will be the shape, size, price and a chinois often has a reinforcing band around the mesh to support it when pushing a product through with a ladle.
For most they will be all you ever need at home.Rosle Fine-Mesh Kitchen Strainers - Sur La Table