For a singer, which instrument...?

I think it's not easy to sing and play an instrument at the same time. It takes time to be good at playing music, and then you have to practice singing as well as playing at the same time.

From the way you say it, I have a feeling you don't play any instrument at the moment. Or do you?

I'd say it's up to you which instrument you want to choose. I myself play piano, but I'm not that good yet, and I certainly don't think I can sing and play at the same time. There are many vocalists that sing as well as play their instruments at the same time. Personally I think the instruments you mentioned are okay, but you should choose what you think would be suitable and comfortable for you to perform with.

p/s: Nothing wrong with your English, don't worry about it :)

For a singer, rhythm guitar or keyboard would be the best choice. They can provide both rhythm and lead parts so it removes the need for another member. I don't think a lead singer should play bass unless they are either very skilled or playing simple music like pop-punk or something. The whole point of bass is to work with the drummer to create a pulse for everyone else to play off of. The bass must be exactly on beat whereas singing does not always have to be. It's very difficult to play complex bass parts and sing at the same time. You're basically building a foundation and working off of it at the same time.

Bass isn't as complex as guitar, and so would be a fairly simple thing to play while singing. Guitar might take more concentration. And keyboard is kind of in between, because it takes concentration to play harder songs, but if it's a simple bit with not much complexity, it won't be hard.

Piano or Guitar, bass can be self taught if you know guitar, piano is the key to all music

It all depends on what instrument you like. Personally, I like acoustic guitar to sing with because it's more calming.

bass is the easiest to play while singing so i would go with that

but if you stick to it learning to sing with guitar playing is better but a bit more challenging

keyboard,or guitar.