Do it right the first time!! Get the HR Parts motor mounts.
If you're on a budget, and your car is lightly modded as you say, then leave it alone until you can save up for the mounts. You don't need a strap unless you know the mounts are totally shot.
The straps are more trouble than they're worth, especially if you snap a mounting point.
IMHO, only going with a driver's side poly mount isn't getting the job done. Sure you have the driver's side fastened well, but now when the torque is applied, the driver's side can't lift so that torque has to go somewhere. Guess where, the passenger side is then pushed down since the driver's side can't turque up. You're litterally forcing the downpipe down and banging around with that mushy stock mount on the passenger side.