Trying to get a concensus
Not sure you'll get a total consensus

, but I like your breakdown based on your market description.
how many shirts per design should one have at start-up?
As with most things: it depends
If you are starting up with a big budget and a big bang product launch (advertising in major media, press, website setup, links ready to go), then you might need a lot of t-shirts on hand (500-1000)
If you plan on starting small and growing, I think 25-50 per design isn't too bad. Anything smaller and the screen printing costs aren't going to be worth it (and you'll have a harder time managing size inventory).
and this costs about $6.30 per shirt. I know this can get better with more quantity...how much better?
Is that just the cost of the printing or the garment and the printing?
The best way for you to answer the "how much better" question would be to call around to local printers and ask for their quantity price breaks for your job type.
I am using Anvil Chromosone at about $3.40 a piece and Basic tees by Anvil and Gildan at about $2.00 a piece....how much cheaper can these get if I am buying several dozens at a time?
I usually have my printer source the blanks for me and include it in the price of the job. I don't have the time or desire to source blanks and have them shipped to the printer. But I've seen prices from under a dollar for white garments (during special offer periods with major distributors like SanMar, SSActivewear, etc).