From your description it sounds like you will need the radiator.
The radiator has a plug you can remove (opposite side from the cap) to let air out while filling it.
After you install it and fill the system with coolant keep an eye on the overflow tank for bubbles. There will be some initially but they should stop after a few warm up and cool down cycles. The warm up pushes air out of the system into the overflow tank. The cool down sucks coolant into the system. After that, if you still see a continuous stream of bubbles then it needs head gaskets.
If this is an automatic transmission check the rubber tranny coolant hoses that connect the lines to the radiator. They usually get very hard and crack when you remove them from the radiator, so you may have to replace both of them.
Changing the water pump and timing belt and components would depend on their age and what brand was installed, it they have been replaced. Your 96 is an interference engine with adjustable tappets on the valves. I would play it safe and do the right thing, new good components.
You can download the Factory Service Manual free from two places.
I use THIS site because you get the whole thing in one zip file. When you click the zip file download button another window will open. It's an add just click the X to close it.
Or you can download individual files HERE.
With this being a 96 and 200k there are 3 small coolant hoses you should check while you are at it. The OE hoses are molded and soft and can swell up and split. That happened on our 95 and 97 EJ22's. They are located under the throttle body and IAC Valve. 2 of them are on the throttle body and 1 goes from the IAC Valve to the coolant pipe where the two temp sensors are. They are not easy to replace. For that last one, I use a hose about a foot long and loop it out around the PVC pipe and IACV.