Tri-X is the old standard in high speed (relatively) B&W film. It has a look that people either love or hate. It is more grainy that many newer films, but that is part of its charm. It can be pushed to very high speeds.(posted 8790 days ago)T-Max is the newer T-grain emulsion. People either love it or hate it. It seems to be a little more critical of development than Tri-X.
400+, I think you mean B&W Select +, which is a C41 processed B&W. This means the film is processed as if it were color print film, but you end up with a B&W negative. Most mini labs end up giving you prints with color casts, but it can still be printed nicely on B&W paper. Due to the color type film/chemisty you end up with reduced grain but the negatives are made up of dye clouds rather than silver grains, so they are not as archival (may not be a problem). It does not tolerate under exposure at all, but it can be pushed (if you can find a lab that will push process color print film).
I would suggest shooting some with each as a test and see which look you prefer. I would also try Tmax 3200 and Ilford Delta 3200 for low light, no flash shots. THese can also be pushed faster.