Placement of Jr. and Sr. with biblatex

The standard biblatex directives to format names use some auxiliary bibmacro:

name:first-last
name:last-first
name:last 

For predefined name formats. Each of these take four arguments: the first is for the family name, the second is for the given name, the third for the "von" part, and the fourth for the "junior" part.

Thus, one can use of the auxiliary format, for example

\DeclareNameFormat{author}{
  \usebibmacro{name:first-last}{#1}{#3}{#5}{#7}
}

For the parameters, \DeclareNameFormat splits a name in 8 parts:

#1: last name
#2: last name (as initials)
#3: first name
#4: first name (as initials)
#5: name prefix (von part)
#6: name prefix (as initials)
#7: name affix (junior part)
#8: name affix (as initials)

If the auxiliary bib macros do not produce the desired format, one has to provide a new definition. For example, a simplified definition for the format in the OP can look like the following:

\DeclareNameFormat{author}{%
  \usebibmacro{name:delim}{#5#1}%
  \ifblank{#5}{#1}{#5 #1}\addcomma\addspace
  #3\isdot
  \ifblank{#7}{}{\addcomma\addspace #7}\isdot
}

author (or other names) are lists, thus \DeclareNameFormat loops over all the elements in the list (up to a limit if give, for example by maxcitenames) and for each name it executes the code it the body of the definition.

Here the first step is the predefined biblatex macro name:delim. This macro takes care of the punctuation between the names. For the first name it does nothing, for successive names it insert a comma an and a comma and and before the last one.

The second step is to see if the "von" part is empty (parameter #5): if it is it print the last name (parameter #1), otherwise it prints the von part and the last name (#5 #1).

The next step is to print first name (parameter #3) (here the definition assumes that there is a first name!), so the separator between the last and first name is printed with e first name. The scope of \isdot is to ensure that a period in an initial is not consider as full stop, and thus the following punctuation is not ignored.

The final step is to check if there is a junior part (parameter #7). If it is not black it is printed. The \isdot is to cover the same situation as before.

EDIT

To use the above definition in a last-first/first-last schema, the above definition can replace the standard name:last-first macro, namely:

\renewbibmacro{name:last-first}[4]{
  \usebibmacro{name:delim}{#3#1}%
  \ifblank{#3}{#1}{#3 #1}\addcomma\addspace
  #2\isdot
  \ifblank{#4}{}{\addcomma\addspace #4}\isdot
}