Where do I put the Supporter card revealed with Random Receiver?
Read the Random Receiver card and you'll see it goes from the revealed cards into your hand before you shuffle. You do not put the card aside face up on the field nor shuffle before putting it into your hand. This applies to other cards that use the "reveal... put it in your hand... shuffle" template like Ultra Ball, etc.
Source: TPCi Rules Team (2013-08-15)
If I use Random Receiver and the very first card revealed is a Supporter, do I still have to shuffle my deck?
Yes, you must shuffle your deck regardless of how many cards were revealed for Random Receiver.
Source: TPCi Rules Team (2012-09-13)