No you will not find a house in that price range. You might get lucky and find one between $800 - $1,000 but houses go for between $1,150 - $1,500 and up. Rental prices are extremely inflated considering most people would rather rent nowadays than buy. I have lived in Arlington my whole life and I can tell you, in my opinion, that Southwest Arlington is probably the safest. The 76016 zip code is probably the most desirable and has the best schools. 76017 is probably the second best zip code, but some homes are located in Mansfield school district. The least safest area would probably be the older parts of Arlington, around central and East Arlington. But again, that is just my opinion based on experience.