Yow! Not askin' for much, are ya?
Transmissions... Let's see... You could go to almost any Mustang parts supplier on the web to get a 5-speed conversion kit for a 66. (Including
Mustang Depot,
Mustangs Plus, and
Sacramento Mustangs, to name a few.) The conversion kits are available separate from the transmission in most cases, so if you're looking to get a 5-speed on the cheap, you *might* be lucky enough to find a donor car somewhere. I've found only two places that have 6-speed conversion kits (which is what I plan to wedge into my 'Stang... you know... on the off chance I can find a place that'll pay a database developer what he's worth...) and they are:
Dark Horse Performance and
JMC Motorsports. (The Dark Horse kit includes the transmission, the JMC Motorsports kit does not. Not that it'll matter since you'll be hard pressed to find a donor car with a T56 in it...)
As for handling upgrades, well, I'm far from the best person to ask on the subject... I depend on others for my information on the topic and I have not gotten to that stage with my car as of yet. I can outline my plan of attack, however. It might help you decide what to do with your car...
Ninjamobile's plan to rule the world with a '66 Mustang Coupe:
1.) Wheels.
195-75-14 wheels have crappy contact patches. 225-45-17 wheels, on the other hand, own.
2.) Brakes.
Four-wheel drums just don't cut it. Four-wheel discs with 13s in front and 11s in the back do, however.
3.) Suspension / Handling.
This is where I get rather less sure... The following I know are must-haves: panhard rod (keeps your back tires from wandering around corners), negative roll camber kit (fixes understeer / oversteer), graphite bushings (stiffens suspension, keeps wheels on road where they belong), export brace (keeps front tires from wandering), and subframe connectors (stiffens car frame - necessary for higher-torque engine).
4.) Differential.
Gotta have a posi. You can get Detroit Locker third members for 8" rear-ends, so I may not need to track down a donor car to get a whole rear axle with a 9" pumpkin on it. I'm thinking 3.51 ratio or somewhere thereabouts. If you really want to kick your gas mileage in the ass, you can go higher, but it's not worth it, IMHO.
5.) Transmission.
I'm going with a T56 conversion, myself, as already stated.
6.) Engine.
Remains to be seen if I will try to upgrade my existing engine or trade it in on a crate with more horses, but I'm looking for something closer to 350hp.
7.) Paint Job.
I have no idea whose bright idea Emberglo was, but when that color fades, there's no "glo" left in the "Ember". It's just a hideous brown. My baby's gonna be Dark Moss Green.

8.) Rule the World.
It's just that simple! :evillol:
As you can see, from this plan, you have to work your way from the bottom up. If you neglect any one of these steps, you reduce the effectiveness of the next step. (Wheels, for instance, are the cornerstone of your car. Without a big enough contact patch, you'll suck on cornering and accelerating. Remember: if your wheels are spinning, you're wasting power.)
If you have any questions, lemme know. I'll be glad to help you out with the specifics...