I use an old, sanitized, two-quart saucepan to scoop the wort out and pour it into the strainer.
I usually use a stainless steel mesh strainer which I sanitize by boiling for the last 15 minutes (I don't trust chemical sanitizers to permeate every crevice in the mesh). The first time I used the stainless strainer plus the finer plastic strainer in my funnel. This gets a lot of the little stuff, but even with two-stage straining is rather slow. I'm now leaning toward just the single straining, or no straining at all, depending on my mood and what I'm making.
If you're going to take the strain approach, why not use muslin bags? I know some people worry about hop utilization but I make sure that I don't stuff the hop pellets tightly at all. I use a small mulsin bag and I tie the knot as near to the end as I can allowing maximum expansion. I still pour through a strainer and since most of the material is in a bag (or bags), the strainer remains clear enough to pour all at once.