Kid,

That's a totally doable swap, but make SURE that you complete the transmission swap BEFORE you haul off the car. There are always a few small pieces that you will need from the donor car that you wouldn't think of.

For instance the front motor mounts are different on a manual transmission car and it would be good to change them. The driveshaft will be different and many little things that you may need that you have not thought of.

The shifter problem is most likely just worn out bushings. Make sure the transmission works well before you go to the trouble.

Good luck,