Reading 4-20ma signal on arduino
Using a resistor is the "Normal" way, yes. 250Ω will give you 1-5V, yes, which means that you get 4/5 of the actual resolution of the ADC at your disposal.

That means instead of 0-1023 you're actually reading 204-1023, or 819 possible values. Spread over 16ma (or 4V, which are the same thing) that gives you about 20µA resolution.

If you really really care about that extra 1/5 of the resolution you can instead use a 300Ω resistor to give you 1.2 to 6V, then pass that through a subtracting amplifier (see this post) and subtract 1.1V from it (you need to create that 1.1V, of course).  That will give you 0.1 to 4.9V, which then covers more of the ADC's available range (20-1002, or about 16µA resolution).

Is it worth it? Probably not. Any increase in resolution will likely be swamped by the inaccuracy of the resistor and potential drift though self heating.