Our doors are pretty heavy, and many years of swinging open and closed has worn the metal bushings out. Some have worn so bad that the door latch is now getting flat on the top because the door is 1/4" or more too low. Or maybe your doorsill is worn and the Body By Fisher plate is all but demolished.
Rebuilding the hinges is fairly straightforward- you can buy bushing kits almost anywhere, the hardest part is wrestling the door on and off the car. Pay off a friend, you'll want the help unless you've got the jigs/tooling. Multiple floor jacks and blocks of wood help, but you can see how this can go wrong quickly. The spring can be a bit troublesome too, and Vice Grips help tremendously, as does a vice.
Before you even start, go ahead and put some masking tape on the edges of your fenders and doors to help prevent chipping the paint. You can remove the doors, then hinges, drill and replace the bushings, and bolt everything back where it belongs. Once you've got the door loosely bolted to the car you line up the rear first and work your way forward. I tape a piece of twine to the body line as far back as possible that allows the twine to actually be a good guide, and tape the other end to the same body line on the core support. Tape it down in more than one place, at least a few inches apart.
Adjust the latch height and horizontal position until the rear and bottom gaps are good. Minor adjustments to the hinge bolts will be necessary throughout that process, and the twine serves as an up-close visual aid. Otherwise you'll constantly be backing 15 feet away to see your changes. This gets tricky and can take many, many tries. Don't be surprised if you readjust the same thing 5 times only to do it again. Feel free to use things like popsicle sticks or paint stir sticks to measure the gaps you're adjusting.
The process continues to the fenders, because you are NOT going to get the doors adjusted correctly without moving the fenders too, especially if you change the core support bushings at the same time. And you should definitely do all of this at the same time.
Personally, I'd remove the fenders entirely then tackle the bushings and hinges, in that order. It makes things SO much easier. That way you can adjust your doors without the fenders in the way. Following that I'd replace the fenders and adjust until the gaps were acceptable. Then don't forget to readjust your hood before slamming it shut, and tighten those core support bolts! It's very easy to forget those last 2 things after playing with all of the other fasteners repeatedly.
For the rattles inside the door: Go to Mike's Montes, Kirban Performance, OPGI, or GBodyParts and pick up "How To Eliminate Window Rattles and Wind Noise" By Peter Serio for $20, and the anti-rattle kit for $45 (x 2).
You can also find places where rubber hose, grommets, or sheets of butyl rubber will prevent other rattles.