Question: I'd like to buy new resistors for breadboarding with my Arduino Uno. There are 0.25W, 0.4W, 0.6W, 1W, 2W, 3W, 5W, 10W resistors in the shop. What is the most suitable for this operation?

Answer: 
Go with 1/4 Watt resistors but be prepared to use 1/2 Watts if the leads don't press down cleanly into the breadboard which is what I think you are asking about. If you need anything in the higher wattage range and you are working with an Arduino, then you are doing it wrong. An Arduino could not smoke a 1/4 watt if it tried.

I have fought for years with our purchasing agent over this at the college I work for. He buys 1/8th watt resistor in bulk, but fails to heed the advice that you cannot use these on standard classroom breadboard without bending the leads at best and failing to even make a good connection at worst. You need reliable connections and 1/8th and smaller are useless on breadboards. Just my two cents from years and years of experience.
The smaller the better for the most part. On 1/4 or 1/8 W resistors the leads size is small enough to work well in bread boards. Rarely do you need to dissipate large amounts of power so 1/8 is a good size for logic, maybe 1/4-1/2 for power supply areas. See Majenko's answer for the heavy math, mostly applicable in power supply areas as he points out.