[Grammar] Would rather /Prefer /Would prefer

[sania-baharat]

Is this analysis OK?

Would rather : Modal verb
Prefer : Main verb
Would prefer : Main verb

Also, I don't know which of the sentences below is correct.

I would rather go to cinema than stay at home.
I would rather go to cinema rather than stay at home.
I would rather go to cinema to stay at home.

 

[tedmc]

I would say:

I would rather go to the cinema than stay at home.

I would go to the cinema rather than stay at home

I prefer going to the cinema to staying at home.

 

[sania-baharat]

Thanks.

Is this analysis OK?

Would rather : Modal verb
Prefer : Main verb
Would prefer : Main verb

Could you please answer this question?