the gas is 5/16, the beer is 3/8 line.
TD
if the line is short (5 feet or so) the beer line should be 3/16"inside diameter, not 3/8"
2.4 v/v or 2.5 v/v CO2 (typical carbonation for microbrew/craft/homebrew ales) at 38deg F would require about 14PSI of 100% CO2 to maintain the correct carbonation level.
To balance your pour speed with this pressure you need 14lbs. of restriction
1 lb for cooler hardware (on a direct draw it is less)
0.5 lb for each foot of vertical rise from the centre of your keg to the faucet
(assuming a beer tower on top of your counter that would be about 2')
that gives us 1 to 2 lbs so far leaving 12 to 13 lbs to make up with choke line.
3/16" ID vinyl tubing provides approximately 2.5 lbs of choke per linear foot
12.5/2.5=5 feet of 3/16" vinyl tubing.
unless you are serving a beer with a wildly higher or lower carbonation level (like Guinness at 1.2 v/v, or some Belgians up to 2.9 or 3.0 v/v) then ALL direct draw/kegerator/Keezer setups should have 5 feet of 3/16" ID vinyl tubing between the keg and the faucet.
with long line systems the rules change and that is where beer gas comes in.
Many bars use beer gas (25% CO2, 75% nitrogen: AKA stout gas) because they require pressures exceeding 18 PSI to push the product from cooler to bar. This allows them to prevent overcarbonation as previously posted, but does not provide sufficient CO2 to maintain carbonation so the beer will get progressively flatter.
Overcarbonation is a major issue in a bar because it produces 'wild' beer and excessive foam which affects the bottom line very dramatically.
Premixed/bottled beer gas in this circumstance is an imperfect solution.
Undercarbonation also affects the bottom line because because it affects presentation and product quality, but must dramatically because if you only have 1/4" of head instead of 5/8" of head then you have given away 3/8" of free beer when you fill the glass.
'SMART' bar owners use blended gas with blends tailored to their dispense pressure (like the McDantim blenders, like the Micromatic blenders (which BTW are McDantim blenders)) So at for example at 28 psi dispense pressure, you can maintain carbonation in a 2.4 v/v beer with a 50% CO2 50% N2 blend. If you have a different dispense pressure then change the blend. Perfect presentation to the end of the keg, consistent product, consistent pour, maximized yield.
BTW. I work in draught system installations and my employer is one of North America's largest Micromatic distributors.