Let's do it. Let's design the whole mezzanine.
Start with the floor sheathing. I like 3/4" T&G plywood, glued and screwed and staggered for the decking. Run perpendicular to the joists and provide solid blocking under all seams.
Joists I like to space at a maximum of 16" on center, to support the floor sheathing properly. I use this calculator for sizing joists:
http://www.awc.org/codes-standards/calculators-software/spancalc
A 40#/SF live load is typical for residential floors. This should be adequate for what you describe. Using that, and a 10#/SF dead load, Spruce-Pine-Fir for material and a deflection limit of L/360, 2x6's will span 9'-5". The actual span is 9'-6", so this will work.
The beam has a contributing area of 6SF x 50#/SF total load, for a total load of 300#/LF. The LL is 240#/LF. I use this chart to size LVL's:
https://parr.com/PDFs/LP%20LVL%201.9E.pdf
Using a readily available 1.9E LVL, a double 11 1/4" deep LVL beam will support a LL of 284#/LF and a total load of 416#/LF, so this is more than adequate. Support with a 4x4 post or 3 2x4's as columns in the walls.
The ledger along the wall needs design as well. I would lag it into every stud, but I also like to support it at both ends and in the middle, with a stud laid flat against the wall and lagged into a stud. This cuts the span in half so you can use a smaller beam. Dimensional lumber will work here. I use this chart:
http://www.awc.org/pdf/codes-standards/publications/wsdd/AWC-WSDD1986-ViewOnly-0301.pdf A 15' long 2x12 will span the two 7 1/2' spans and support a 362#/LF total load at a L/360 deflection limit, so this will do.
Understand?
Bill