Kodak TX 400 (also known as Tri-X 400) is my bread and butter of B&W films. With an ISO of 400, this 35mm film provides a lot of flexibility in lighting situations and has a great range for exposure. It is a very forgiving film so it is perfect for those days when you carry your camera around but don't know what or where you will end up shooting.
When I took my first photography class the film my teacher told us all to buy was Kodak Tri-X 400. This film has the classic black-and-white grain quality with wide exposure latitude, giving information in both the highlights as well as the shadows.
Armed with my Grandfather’s hand-me-down Canon AV-1, I have used this film in all types of conditions: indoor and outdoor, overcast and sunny, action and still, and am usually happy with the outcome. With the right exposure, the grain can come out very fine and the tonal changes are rich. With improper exposure the grain can be more prominent. Grainy is not a bad thing though; I think it gives the photographs a more newspaper feel with a higher contrast. I have blown up some of theses 35mm negatives to 16×20 and the grain still looks good at that large a size print.
I highly recommend using Kodak TX 400 whether you are just starting out or are looking to try something a little more versatile. It can come out a bit gray when shooting thing in the same tonal group, but as long as you have some variation in either color, texture, light, focal point, etc., the film comes out well. You really can get 36 good frames on this roll no matter where you end up with your camera.