This is the correct way to ask the question, but it is hard to answer.
First, we need to establish the weight carrying capacity. 30 pounds per square foot (live load) would probably be a minimum number. 10x13x3900 = pounds. Building to less than that leaves you open to future lawsuits.
The problem with lag bolting ledgers to the wall is there is TOO MANY VARIABLES ! What size lag ? What size pilot hole ? How deep does the lag go ? The simple solution is, install the ledger, but run some 2x4 laid flat against the wall from under the ledger down to the floor over each stud (16" O.C.). Either use PT of have to bottom sit on a piece of PT.
Checking the SYP Span Table, if the joists are going to be 10', you can use 2x6s 16" O.C for joists. Your corner post can be a 4x4 or 6x6, but the joist either have to rest ON TOP or be NOTCHED IN to the post. You can probably use 5/8" plywood. Same tables says if your use 2x8, you can go 24" O.C. I would go back to the 3/4" plywood and you will need blocking under the plywood seams.