find . -type f -print0 |
  rename -n -0 '
    s/[- ]*_[- ]*/_/g;      # get rid of spaces and - before and after _
    s/([ _.]){2,}/$1/g;     # reduce multiple space, _, . to just one
    s/[\@\$!]//g;           # remove @,$,!
    s=(\.[^./]*$)=lc($1)=e; # lowercase filename suffixes
'

The first substitution (s/[- ]*_[- ]*/_/g;) assumes that you don't want spaces before _ even though you only mentioned removing -s before _. Change it to s/-*_[- ]*/_/g; if that wasn't what you wanted.

find . -type f -print0 |
  rename -n -0 '
    s/[\@\$!]//g;            # remove all @, $, and ! characters.

    # remove leading and trailing whitespace (if any) from filenames
    s/^\s+|\s*\z//sg;

    # change all runs of any whitespace to just one space
    s/\s+/ /sg;

    s/[- ]*([._])[- ]*/$1/g; # remove space(s) and - around _ and .

    s/\.\.+/./g;             # reduce multiple periods to just one
    s/__+/_/g;               # reduce multiple _ to just one
    s/_*\._*/./g;            # change _. and ._ to just .

    s=(\.[^./]*\z)=lc($1)=e; # lowercase filename suffixes
'

The third substitution replaces runs of one-or-more of any whitespace characters (including actual space characters, tabs, newlines, form feeds, etc) with a single space character. IMO, even though it's more than what you asked for, replacing all the different kinds of whitespace characters in the filenames is probably more useful than just replacing space characters. Change \s+ to + (two spaces and a +) if that's not what you want.

The fourth substitution (s/[- ]*([_.])[- ]*/$1/g;) assumes that you don't want any spaces or dashes before either _ or .. That's more than you asked for, but is easily changed if it's more than you actually want.

On a related note, the second-last substitution replaces _. and ._ with just .. This is so you don't end up with "ugly" filenames like foo_.bar_._pdf. Delete this line if you want filenames like this.

Using find and perl rename:

Note: perl rename is also known as file-rename, perl-rename, or prename on various Linux distros. Not to be confused with the rename utility from util-linux which has completely different and incompatible capabilities and command-line options.

find . -type f -print0 |
  rename -n -0 '
    s/[- ]*_[- ]*/_/g;      # get rid of spaces and - before and after _
    s/([ _.]){2,}/$1/g;     # reduce multiple space, _, . to just one
    s/[\@\$!]//g;           # remove @,$,!
    s=(\.[^./]*$)=lc($1)=e; # lowercase filename suffixes
'

The first substitution (s/[- ]*_[- ]*/_/g;) assumes that you don't want spaces before _ even though you only mentioned removing -s before _. Change it to s/-*_[- ]*/_/g; if that wasn't what you wanted.

Note: rename's -n option makes this a dry-run, only showing what it would do. To actually rename the files, remove the -n or change it to -v for verbose output.

Also note, the multi-line rename script can be squeezed into one long, almost unreadable line if you want (if you delete the # comments), but the extra line-feeds and indentation make it easier to read and edit, both on the command line and in a script.

Finally, this assumes that when you said "go through each file in the directory/subdirectories (skip any symbolic links)" that you also wanted to exclude directories, device nodes, named pipes, sockets, etc from being renamed - i.e. rename only regular files.

If you wanted to rename matching directories too, you'd have to change -type f on the find command line to \( -type f -o -type d \).

You can, of course, use whatever find predicates you like to refine the search.

Using find and perl rename:

Note: perl rename is also known as file-rename, perl-rename, or prename on various Linux distros. Not to be confused with the rename utility from util-linux which has completely different and incompatible capabilities and command-line options.

find . -type f -print0 |
  rename -n -0 '
    s/[- ]*_[- ]*/_/g;      # get rid of spaces and - before and after _
    s/([ _.]){2,}/$1/g;     # reduce multiple space, _, . to just one
    s/[\@\$!]//g;           # remove @,$,!
    s=(\.[^./]*$)=lc($1)=e; # lowercase filename suffixes
'

The first substitution (s/[- ]*_[- ]*/_/g;) assumes that you don't want spaces before _ even though you only mentioned removing -s before _. Change it to s/-*_[- ]*/_/g; if that wasn't what you wanted.

The e regex modifier in the last substitution causes the replacement to be evaluated as perl code - in this case, the lc() function, which lower-cases its input.

Note: rename's -n option makes this a dry-run, only showing what it would do. To actually rename the files, remove the -n or change it to -v for verbose output.

Also note, the multi-line rename script can be squeezed into one long, almost unreadable line if you want (if you delete the # comments), but the extra line-feeds and indentation make it easier to read and edit, both on the command line and in a script.

Finally, this assumes that when you said "go through each file in the directory/subdirectories (skip any symbolic links)" that you also wanted to exclude directories, device nodes, named pipes, sockets, etc from being renamed - i.e. rename only regular files.

If you wanted to rename matching directories too, you'd have to change -type f on the find command line to \( -type f -o -type d \).

You can, of course, use whatever find predicates you like to refine the search.