You're much more organised than I am RobsonValley
I use a couple of sprouter jars, we can buy the grated lids on ebay that will fit any of the Kilner jars, but my old spouter has a kind of angled rest on it that keeps the jar gently draining. I just rinse it through with fresh water every time I pass the kitchen sink.
About a week to get biggish shoots, but just sprouted grains can often be a couple of days. The kitchen's pretty warm.
You're right about the garden seeds, but saved home grown seed is fine.
When I started growing sprouts all those years ago I just used a bit of net curtain and an elastic band to make a 'lid' for the sprouter jars. Any really porous cloth will do though.
I have never had mould or fungus on my sprouts. Seriously, in all these years I have never had mould, and I don't own a dishwasher. In this house everybody washes their own dishes in the kitchen sink. I do wash well and dry thoroughly though.