Going from 83gi to 77.5gi is VERY noticeable, but you may want to go to 72.5 anyway.
My suggestion is to just go out and get both cogs, try them both and see which you like...for now.
Your fitness level and riding terrain will probably change over time. You may want to swap cogs.
3/32" or 1/8"? your choice. Frankly I run 1/8", but I put in a lot of miles and haven't ridden a geared bike in years.