can anyone tell me what application to open my downloaded programs with? I have MacOSX v.10.4.7 and when I download programs, it asks to "choose an application" to open the program with and I don't know what to chose

We need to know what extensions the files have.
For audio files, I'd recommend iTunes.

For .SIT files, I'd recommend StuffIt Expander.

For .dmg files, I'd recommend Disk Copy.

For zip files, go to File menu & choose Open with BOMArchive helper.

For video files such as avi, mpg/mpeg, wmv, I'd recommend this player VLC - (click on link).

To change the default program to open particular files, see the example here How to change default program in OSX. If you do this, then it will automatically open with those programs as soon as you double-click the file.

Any other file types let us know.