I recommend over seeding your hillside with a desirable annual. In our area, auburn alabama, i would use rye or brown top. An acre of seed would cost about 25.00. The over seeding will help keep out the weeds. This is not a perfect solution, but less expensive.
Plant some type of tree. For us, we would use Crape Myrtle, Vitex, maple or pine. These will grow and give you a canopy which over time will shade out weeds. Order 'whips' from a forestry supply company. Put these on drippers so they grow quick.
If you look at a forested mountain hillside you will get an idea of what you are trying to mimic but on a smaller scale.
Plant these trees on about a 5' center. It is tight but you want that canopy fast
