Of the few homes actually on the Boulevard, you will be lucky to find any for rent. Those are homeowners. If they had to rent it out, and cover their mortgage, you would be paying at least $3500 a month, but more likely $4500-$6000.
More likely, if you want a home, you need to check on the interior boulevard streets, so the 2 blocks north and south of the boulevard, between rockwell and kedzie. Don't forget to check between fullerton and milwaukee, west of Kedzie to central park. Lots of great single families here, convenient to Logan things.
Expect to pay a minimum of $2000 for a dated, small single family home. For better condition, you will be looking at $3000 and up.
Alternately, you can pick up a 3 bedroom apartment, dated, for as little as $900 a month, with luck.... more