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What distance are you shooting? Get a barrel manufactured to like 8 inches if you want it short and light, just keep overall length legal and go super short or chop it to 18.5 inches plus a bit to stay legal.
 
The higher the expansion ratio (the bigger the bore) the less velocity loss per inch of barrel. I bet you would only lose 25-30 FPS/inch. Pretty negligible.
 
I think 20" is probably the best trade-off for velocity/accuracy vs compact handling... I would not go shorter as it will affect the value/desirability should you decide to sell down the road.

You did not mention what action you are building the rifle on?
 
20" sounds like a good length.

The fatter the bullet, the quicker it gets up to speed, and if your utilizing your powder better (which you would be for 20") the more reasonable the percussion.

For something like a .243 or 6.5, youd want longer, 21 or 22 min-for those who dont shoot with hearing protection.

You would probably be happy with something as short as 17 or 18", but I'd go with 20 personally.
 
I'll be the odd man out and say leave it longer, for now. Once you actually get hands on the rifle you'll know for yourself if you want to shorten it or not, and it is much harder and more expensive to add length to a barrel than a cut and crown job. Your choice though, I have a feeling that for your intended uses a 20" barrel will prove capable.
 
As an example this is my 14" barreled T/C Contender carbine in 338JDJ #2 my loads are 180gr Accubonds @ 2500fps and 200gr SST's @ 2350fps.

I could load the 200gr SST's to 2400fps but they are so accurate I left it alone the 338JDJ #2 has a larger case capacity than a 338 Federal but I can only load the Contender frame to a max 45,000psi where you can go much higher 60,000psi with the 338 Fed.

I consider this combo a 300 yard capable big game hunting setup the 180gr bullets are still doing over 1800fps @ 300 yards.

If I was to build a 338 Fed I would go max 18" barrel.

 
I rebarrelled a Wincester Model 88 to 338 Federal a couple of years ago, and went with a 20" barrel. Built this rifle specifically for bear hunting and bear watch work. Using the Federal Premium 210 NP ammo exclusively. Has a rear ghost ring site on a rail and a Trijicon front sight for low light work. Currently has a Leupold VX-3 1.75-6 scope in qd rings mounted on it. Took a nice caribou with it last month. Haven't had much time for bear hunting of late.

Chose 20" as that is also what my Browning BLR in 358 Win has, and I really like how it handles. It has been my main back-up guiding/archery/atv/horseback rifle for 15 years and has accounted for lots of game, from deer, moose, elk, black bear and grizzly bear.

As a lefty, I really like the levers, and like detachable magazines too.
 
I've had a couple of Feds, my current one has a 24" barrel. I would not go below 20". I'm currently getting 2550 fps with a 225 gr Accubond and a max charge of Hogden's LVR, 2510 with CFE 223. 100fps is the difference between a 400 yard gun and a 500 yard gun. With high BC projectiles velocities matter for low level expansion. I've take game cleanly at over 400 yards with the above combo, great mountain caliber when in bear country. I snicker to myself when I hear talk in the gun shops how the Fed is a good brush gun for deer inside 200 yards.
 
I was having this exact debate.. have a nice new Big Horn TL3 incoming and am strongly considering the .338 Fed as my heavier caliber option. All things considered, I think 20'' will be my final answer.
 
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