OP, a few things:
1) DCPS really starts in PK3/PK4, which is to say your kid will be vying for very, very few spots available. It's akin to having your kid lottery into the 2nd grade.
2) Look at past waitlist lines to get a sense of how likely some of these choices will be.
3) Spend some time on
http://www.myschooldc.org/ which will explain how it works and will give you info on each school.
4) Consider private if you don't get into any school you like. The reality is that parents do drive all over the city or move on behalf of their kids and the schools they want them to attend. I'm a little surprised that you hadn't thought of all this before selecting your housing.