What tube should I use for a kitchen rail?
You could accomplish hanging a total of 8 kgs of pans on a 2.5 meter long tube of 25.4mm diameter x 1.2mm thickness. I assume this is the cheapest option, but it might be more susceptible to failure in the long run than your other listed options. Supposing that it was mounted well, it could withstand a good amount of static force... based on my familiarity with materials. I'm a scientist and I'm darned good at physics, but this question is more about familiarity with materials and kitchen rough-housing. 

Generally, 2.5 meter a tube that is 25.4 x 1.2mm will hold your 8kgs of pans, but the 25mm x 3mm tube would destroy the 25.4 x 1.2mm in a "sword" fight. And although the 20mm x 3mm would probably beat the 25mm x 3mm in a sword fight, the 20mm diameter would not necessarily win the load bearing contest against 25mm pipe. So they are about equal except the smaller diameter tube should be a litte less susceptible to dents... it's probably more of an aesthetic choice for size.

If the prices aren't very much different, the 20mm or 25mm x 3mm will be about 6 times stronger than the 25.4 x 1.2mm. Also, you want to have a good stainless steel in the kitchen, like 316.