I am going to open a movie review website where users will publish their reviews,...
To make this successful, you should have at least someone to moderate the reviews, otherwise duplicate content could get posted and/or malicious scripts could get posted and then executed on the site if the input is not automatically filtered. (for example, accepting HTML tags such as the SCRIPT as part of the review message)
but first I need to insert some info about the movie. I need to copy some information from sites such as IMDb, and then I want to refer the website possibly with a backlink. Will it have any bad effect on my site in terms of Google page rankings on Google search?
As the other answerer stated, don't copy content. However, if the content being copied is about one sentence or less and not used too often on the website, then its acceptable because then you're referring to a quote. If however you're taking paragraphs of information or even more, then that counts as duplicate content.
The best case scenario for having duplicate content if you're extremely lucky will be that you'll appear at the very bottom of at least one search engine you attempted to index the affected pages in.
The most likely scenario will be that you will not be indexed at all, and if someone finds you stealing content, they can file a DMCA report on you. I'm not from the U.S.A., but in U.S.A, they call it DMCA. See http://en.wikipedia.org/wiki/Digital_Millennium_Copyright_Act
To best answer your question, the best way to write information about a movie is to watch the entire movie yourself then write about your own experiences about it. If you must copy things, copy maybe one sentence a character said that was exceptional and use the movie title names and actor names.