Solution Methods in Fluent
 

Which solution methods should i use for simulating Pump sump model ?
I have attached images for your reference, please have a look.

By solution method i mean, for pressure "Second order", Second order upwind....

Your question cannot be answered in general. Specially, when you give so few information about your setup.

Normally, the higher the computational order, the better are your results, but this is not true for every possible case.
If you don't do any special high accuracy calculations - just try the defaults. You can also try whether your grid is stable when using 2nd order or not. This should (again: usually) be much better than the defaults.