Landlords always struggle with the criteria they use to select tenants. One of the biggest controversies is whether to take pets. Some landlords are fine with pets while others have had bad experiences with pets and will not take them under any circumstances
Some landlords have taken pets in the past and had no problems, so they are ok with taking pets in their units. While others have had nothing but issues with pets and therefore, refuse to take them.
One recommendation is that if you do take a pet, that you get a security deposit in case there is any damage. Note, that you can only take a security deposit up to 1 month's rent. No more.
Also, make sure you check with your insurance company to know what type of dogs they consider dangerous. If a dangerous breed dog is on your premises, they can cancel your insurance, so you need to be aware of what they consider danagerous.
When make a choice, it's really a personal preference on how you want to proceed with regards to pets. Know what works for you.