Do you mean grad school in the US? If so, your chances are based mostly on getting excellent grades, rather than on the name of the school you attend for undergrad. Both of these schools will give you the opportunity for an excellent education.
It really depends. It is a personal decision, and it depends on what your family can afford. Is this affordable for you family?
Also keep in mind that if you do want to attend grad school in the US, that this can be very expensive, so it is good to save some money now.
You can get a temporary visa to work after graduation, but an employer will need to sponsor you. Sometimes it is possible, sometimes it is not. The thing is, however, that the political situation has changed in the US in ways that directly affect things like immigration, accessibility of visas, economic considerations for employers, etc. It is changing almost daily, so there is no way to predict what the situation will be like when you graduate in four years. For this reason, I would NOT assume that you will be able to stay and work. Maybe you will. But do not assume that you will.