I'd run the carb I'm running now, the adjustable jet carb from the Tecumseh H35. if the 2hp is similar to the briggs then the tec intake manifold will bolt right on with 5min of grinding the holes. Adjustable main jet!! And they are only around $15 a piece. Believe me you WANT adjustable jets!
Carb
http://m.ebay.com/itm/Brand-New-Eng...-H50-H60-HH60-632230-/262236414269?nav=SEARCH
Intake manifold
http://m.ebay.com/itm/Tecumseh-intake-pipe-28416A-H30-H35-HXL35-HSK40-HSK35-/390185601384?nav=SEARCH
For my 3.5hp the needle settings are main 3/4 turn out, idle 1 turn out.
Reason I say it's good is cause it feels a bit small for my engine, it's got a Venturi size of around 12mm. I'd like to upgrade to a larger carb maybe 19 or 20mm.