Remove and replace radiator

Piece of cake. Book time is about 1.5 hours.

Park the car so it is level. Put a drain pan under the lower radiator hose. Loosen the clamp and use a hose pick to loosen it and pull it back, You do not want to pull it fully off, just enough so it has a gap at the bottom so the coolant can drain out. Now take the cap off the radiator.
Next remove the upper radiator hose. At this point you should probably change the thermostat as well. That is part 6. Two bolts to remove the housing. Remove and replace the thermostat.

Next thing is to remove the fan shroud it just bolts in, slide the shroud back onto the water pump. By now the radiator should be drained out. Now you need a tubing/flare nut wrench to remove the two cooler lines that screw into the radiator. Put a different drain pan under those and remove the top one then the bottom. If you can find something to put over the bottom one it will not leak as much transmission fluid as you change out the radiator. Unbolt the radiator and tip it back just to be sure it is empty. Then lift it out with the hose fittings up to keep any coolant from getting spilled.

Now I would replace both upper and lower hoses due to age. Plus the heater core hoses as well, for the same reason.

Now just reverse the process to install the new radiator. When you finish be sure to check the trans fluid level. Depending on how much it leaked it could be half quart low.

Thank you!
What about flushing the engine is it necessary or is it something that I could do after and if so how long after I replace the radiator should I do that? Also, a tubing/flare nut wrench?

If you're doing a flush, do it with the old radiator. A flare nut wrench is a box end wrench with a section missing. It allows you to grip the tubing nuts that hold the trans cooler lines better so they don't round off.