The more expensive name brands are usually more sensitive and can detect pregnancies a few days earlier. But nothing can detect it right away.
The usual recommended time frame to use one is one week after when you expected your period.
If you can't afford one, or you can't buy one, every Planned Parenthood clinic I know will perform a free pregnancy test. Plus afterwards - if you want - they will give you unbiased counseling to help you, whether or not you are pregnant.
Hope this helped.