How do I manually sort articles?
Title a,Title b could be terms of a vocabulary
add this vocabulary as term reference to article
edit your nodes to include desired term
modify front page view to group by term on this vocabulary


to have specific sorting for each of the term articles you can add integer field position to article and use it as sorting criteria in the view

for ordering the terms sort them in the vocabulary term list and use term weight as sorting criteria on view

For sorting one could also use draggable views  and even nodequeue as suggested in the comments