Check my link to Bruce Deuley's compost tea maker design. I have the full plans on a .pdf file you can download and save. The plans are for a 5-gallon bucket but if you have a modicum of imagination, you can see how to make a 55-gallon version with a larger air pump. Hint: use 4 feet of black plastic soaker hose for your 55-gallon version "air stone." Then throw it away after every 5 batches because it will get contaminated beyond useability.
Dr Ingham has seen this 5-gallon tea maker in action during a class she held in Austin last October. She liked it and asked if she could post the plans on her website. I'm not sure where that discussion is, and actually she may have linked to my website and I just don't know it. There's not enough time for everything.
Here's the link.
To answer your question, take the compost that smells the best. The best compost smells like a forest floor after a rainstorm. Anything that smells maneury, moldy, rotten, or otherwise bad is not ready for tea yet.
A lady named Betsy Ross (imaginative parents) lives on a ranch just north of Austin. She sprays 100-200 gallons of tea every day to cover her 500 acres 4 times per year. She makes her tea by straining the compost going in, and she doesn't screen anything after that. Everything that goes into the tea comes out the nozzle. She has a JD Gator with an ag sprayer and a #20 nozzle. That's a huge hole so nothing gets caught in it. She directs the stream against a flat plate at about a 45 degree angle which disburses the spray. With that huge hole she can get her spraying done quickly.