[G4] Ownership and Group settings for Applications folder?

[Mr EMan]

I am having problems with ownership of the
Applications folder having bought my 15" Alum. from an
Army buddy, reset the master password, created my user
accounts and deleted his old ones.  A couple
reinstalls and updates later I keep getting "Do not
have permission" alerts when trying to copy things to
my application folder and sometimes when launching
programs. Running the latest 10.4.

As a expedient fix, I changed ownership to my usual
user account along with all the enclosed items--yes I
know impulsive and likely unwise.  Everything seems to
be working but, in an act of contrition I am wondering
what the usual "ownership" settings are for the folder
and contents.  They were Owner: System Group: Admin

When I change ownership back to system it says no one
can read or write to the applications folder but I
seem to be able to at least to most applications.

So the other questions are: Am I screwed and if so how
badly?  What are the correct settings/procedures to
purge a former user's installations and pitfalls for
correcting?

Eman