You want the tranny with a 24" overall case length, or a 14" tail housing length with the shifter mount in the mid or end part of the tail housing. Galaxy's and later fairlanes used the longer tranny, 27" long, with a 17" tailshaft.
If you are going with a 3.54 rear, you will want a close ratio tranny. If you go with a 3.07 rear, and use a wide ratio tranny, you will have the same first gear overall multiplication, for the same launch, but now have a little better cruising rpms. 2nd gear, the 2nd gear from the back will have 28 teeth if the tranny is a close ratio, and 31 teeth if it is a close ratio. You can't always go by the tag, as many trannys have already been rebuilt, using mismatched parts, and the tag doesn't always guarentee what's inside. When inspecting a tranny, the gears should gradually get smaller starting from the back of the tranny going forward. If not, then the tranny maybe an overdrive toploader from the 70's, and is worth about $50, as you will need to replace many parts to change it into a wide/close ratio.
You can use a small in / small out tranny, as used in small blocks and 390's. Just make sure the output shaft is 28 spline, and not the 25 spline, otherwise you will have to replace the mainshaft as well. I know builders who put these behind 427's and don't have any problems. You can easily convert a small input to a large input by replacing the input gear and front bearing retainer, and keep the small output just like the original 427 cobra's. I believe the small input shaft was the weakest link in the small spline toploader. Boring out the tailshaft to change a small output to a large out is going to cost, including the cost of buying a large output mainshaft.
You will pay more for the big in / big out 24" tranny core, usually hundred's more. Therefore, it may be cheapest to buy a small in ' out tranny core, and rebuild it to a big in / small out tranny. But, if you want the big in / out tranny, you will spend more money.
Regarding rebuilding a toploader, replace 2nd gear no matter what. If you reuse all other parts, you've spent about $250. Replacing to a bigger input is another $200. Any gear chipped or with surface rust needs to be replaced, as the gears are case hardened. If there is any pitting on the inner bearing surface in the cluster gear, it needs to be replaced. Prices add up quickly. Don't forget the shifter. Expect about $400 more for this.
When you buy a rebuilt tranny, you have no idea to what extreme the rebuilder went to. People will reuse rusty gears, or file down the worn syncro teeth and reuse the gear instead of replacing it. The great deal you think are getting with a low priced rebuilt rtanny may not be as great of a deal for what you are getting.
I've met and bought alot of parts from David Kee, and he is great to deal with. You won't get taken, whether you buy parts or a tranny.
www.4speedtoploaders.com
I've also bought parts and a shifter from Mark at
www.toploaderheaven.com , and he is excellent to deal with as well. Dan William's shifter has a cast aluminum adapter block that repositions the shifter correct for a 427 car. Mark builds a shifter that instead of bolting the adapter to repositon the shifter like Dan William's, his shifter has a welded bracket that repositions the shifter. It can't come loose.