Body lift? 4x4 suspension?
Listen, I'm an offroad guy, and I don't see how this pertains to a kart.
A body lift (assuming you HAVE a body) does absolutely nothing for you except make a little more clearance in the fenderwells for larger tires. Has bugger all to do with offroad performance or trailability.
As for "4x4" suspension, you still haven't told me what you mean. There are dozens of suspension designs used in the "froading" world, ranging from semi-, quarter-, and three quarter- elliptic leaf arrangements on solid axles (even transverse), to insane long travel crossovers, to unequal length A-arms with coilovers, ladder bars, torque tubes, torsion bars, bags, leading- and trailing- arms, you name it. All of this stuff can be used on 2wd arrangements, too, so frankly I wouldnt refer to them as "4x4 suspension".
So... what're you after?
One final point-
If you can afford a $1000 budget, you can afford to purchase some professionally-engineered plans. Make sure you have the fabrication skills- this goes a wee bit beyond simply working on cars or sleds. Option #2 for you is search online for a chassis that meets your needs, and drop your engine of choice in there. Not to put too fine a point on it, but I would suggest you do exactly that.