Which rodent is best for adopt, eg. rats, mouse, hamster etc whats their advantages and disadvanages and how to train them to go to toilet?

Of all the common pet rodents, rats are certainly my choice.
They are very smart, fast to tame and learn and will form a strong bond with their human keeper.
Potty training,,well, I have never successfully done that short of having a particular corner of their cage to take care of business. Out of cage, they are going to relieve themselves when and where the urge hits.
Adopting rodents, usually they are already tamed and socialized, so that task is not always needed.
Other than hamsters, male mice and rats, they should all be kept in pairs or more.
They are very social animals and can get depressed and lonely by themselves.
I have found female rodents to be more active and aloof over males.
The males, seem more emotional and confident, a better candidate to cuddle with you, but being emotional, in trick training may get frustrated and give up if they don't understand what you expect from them.
Getting a rodent from a breeder or store, with rats, I suggest as young as you can find, they are rarely socialized and will need taming and trust training to feel safe with you. rats, 4 to 5 weeks old, after 6 weeks, they are young adult and more set in their ways so taming is a bit more of a chore. Basically, any age after they have been weaned, but not more than a week after for rodents.
Which is best is your call, I wouldn't turn down any. if you are new to keeping rodents,I suggest doing some reading about each, and there are keeping forums that area good place to glean information for a specific rodent.
Do a little homework and decide what pet best fits your lifestyle.
Hope this helps.

hi rats over hamster
maybe try pets at homes they are pretty good