3"x2" will be okay but will have to put more noggins in for strengthen as its thinner.Most common stud walls are 4"x2" for sound quality with 100mm wool insulation and 5"x1" door lining fit just right with plaster boardboards on each side. Like I say 3"x2" will be okay but more work depending if you're having door frame etc.
This would be ok for a non load-bearing partition wall. You can double skin each side with 12.5mm plaster board this will give you extra fire protection and you can use a 125mm door lining if needed.
Mark a plumb line at both sides where you intend putting the wall.
Pull a chalk line top and bottom of the plumb lines(floor & ceiling).
measure the width top & bottom (floor & ceiling) using the shortest measurement minus 10mm cut two lengths of timber (head & sole plates).
lay them side by side with there ends flush and with a square mark your stud positions at 600mm centres starting from one end.
Measure your floor to ceiling height minus twice the thickness of your timber minus 20mm extra!
Now lay out your frame on the floor and nail together stand it up position and plumb it ( you will have to cut some wedges ) wedge in place and fix with screws and plugs.
Note You will have to work out any door openings on door width, height ,lining thickness, use 32mm x 125mm or buy a lining set. Always check for wiring and plumbing before drilling
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