Hi hatter78.
Not knowing your background in wood and metal working I'll assume you have a general, but not a full knowledge of them.
There are two different kinds of kits.
The ones like you mentioned made by Traditions and the "box of parts" "kits" supplied by places like Track of the Wolf, Chambers and Pecatonica River.
The first kind are basically factory guns which were semi-finished by the factory leaving the final fitting of some parts, sanding the wood to match the metal parts, some finishing on the metal parts and applying the finish to the wood.
These kits could be assembled with not much more than a bunch of sandpaper, some screw drivers, perhaps some alcohol based wood stain and a finish coating like boiled linseed oil.
Most likely the end result would look pretty good if you take your time.
With a little extra effort you can make some modifications that will make the gun more personal.
Of course, things don't always go as smoothly as one would like so a few other tools may come in very handy, even for building a semi-finished Factory kit.
The first thing I would recommend is a good Hobby knife like an Exacto. They make two sizes and I recommend the larger one that takes a #2 pointed blade. These are great for making small cuts to get the lock, trigger guard etc fitted because sometimes small bits of wood need to be removed.
A 1/4 inch wide wood chisel is always handy. Get the best that the store has. Cheap poorly made imports are never a good buy.
A 10 inch flat mill file is sometimes needed to adjust metal parts and to remove some of the cast surfaces that are sometimes on the metal parts supplied.
Sandpaper isn't just sandpaper. There are sandpapers made for working on wood and sandpapers made for working on metal.
Of the woodworking sandpaper I like the red colored "garnet" paper better than the white "flint" or "Aluminum Oxide". It seems to last longer and cut better.
You should have some 80, 120, 180 and 220 grit woodworking sandpaper. If you can't find all of these that's ok. There is some overlap in what each of these can do.
Of the metal working sandpaper I much prefer the black "wet/dry" silicon carbide to any of the emory papers. The silicone carbide is much harder and lasts far longer.
You should look for 120 or 150 grit, 220 grit and 320 grit paper. When you are applying the finishing coats of oils to the wood you might also want to get a sheet of 600 or 1200 grit but remember, these fine grits are really only good for the final light sanding needed on the finishes.
As for your selection of a Traditions from Dixie, you may want to shop around a bit.
Dixie Gunworks is a wonderful place with lots of things avaiable but their prices are often more expensive than other suppliers.
Don't forget to look at the Lyman Kits.
They are a little more expensive but their quality (over Traditions) is usually better.
I think Thompson Center is still making kits too so you might want to try to find one for comparison.