Insulation itself (the batting) must be cleared from direct contact with electrical or heat sources.
The paper on the insulation must be removed within several inches of any electrical or heat source because the paper is flammable. . . generally 3" of paper removed from around sockets and lighting fixtures is acceptable (not wire, though, wire itself running up the wall - or across - can be in contact with the paper because the wire is properly insulated with it's jacket. The only are to concern with is near the connection, where the wire jacket has been removed to attach the wire to your switch/plug/etc) - but for near stoves and fireplaces the entire paper must be stripped within several feet. I've found it just safer to strip the paper off the entire wall and save yourself some possible regrets.
What type of insulation you need depends on what type of house you have (brick or no brick), the thickness of your walls, and where you live because your climate/existing heat/cold barrier - which is why Scuba asked those things