While there is some merit to the the advice to go to craigslist, I have found that as an agent I have a little more negotiating power for my renters. Properties that are held by investors and managed by property management companies tend to have much tighter restrictions on their rental agreements but if you have an agent who will go digging for you to find a property that is more likely to take all the animals then you have the best of both worlds. Bear in mind though that you typically have to pay a deposit equal to the first months rent for a house, plus a higher non-refundable pet deposit.
Think about buying. Contact me about a program BBVA Compass has for teachers: 3% down payment, no PMI, all funds, including the down payment can be gifted! You may find your mortgage payment will be less than what you pay in rent. My office number is 972-705-2806.
I recommend seeking the help of a REALTOR, who will help you through the entire process! Many folks think they can go it alone, but please remember, buying, leasing, or selling a home is not a simple task. I wish you the best in your house-hunting and thanks for being an educator, you are a hero and role model :)
Like some have mentioned that the 3 pets would be an issue but you will have to prepare for a double pet deposit. They usually runs about 250-300 per pets. So you just have to save up and able to put down a big deposit.