Full suspension bikes are notoriously difficult to build. If you use a rack, definitely make sure you have the tire clearance. You will want a minimum of 100mm clearance, or if your bike of choice has more travel than 80mm, add 20mm to the wheel travel and that's the clearance you will need.
Now, as for the 2 stroke engine: you'll have your work cut out for ya. You will need a way to route the chain forward from the rear of the engine in order to use a shift kit. You could jimmy rig a sick bike parts 4 stroke shift kit to mount into that frame, but there's no guarantee there. Your best and easiest bet would be to use a couple idler pulleys, several spring loaded tensioners to keep tension in the chain when the suspension actuates, and a direct drive sprocket. If you could post a photo of the bike you want to use, I would be able to better tell you what would be needed to make it work.
There are a few comfort cruisers out there with 30mm travel in the rear that would fit a motor, but they're generally made of aluminum and light duty.