Pet (and People) Friendly Pest Control
However, within your unit you can choose your own plan of attack. Here are some pet (and people) friendly pest control methods:
Cleanliness is Next to Godliness
Your best move is to prevent pest invasion in the first place. The kitchen is the first place to start. Do not allow dirty dishes to sit in the sink overnight. Sweep or mop regularly to reduce crumbs and other debris. Store food items in plastic or glass containers.
Fill the Gaps
Insects and other pests can enter your apartment through tiny cracks or holes. A small dab of caulk can prevent entrance through small cracks. Mice can squeeze through larger holes. You can deter them by purchasing steel wool and pushing it into the hole. For larger gaps and holes, contact your landlord and request repair.
There are a lot of traps on the market. Choose the solution with the fewest chemicals. Or, search online for DIY recipes for natural traps.
Folklore says that eucalyptus and wormwood are known for repelling animals and insects. Some have had success covering carpet with lavender for an hour, picking it up, and then sweeping up fleas and their eggs. (According to this logic lavender supposedly puts fleas to sleep). Even if you're not prone to witchcraft a natural solution might be superior... or at least provide a nice scent.
Finally, this site details natural pest control solutions for specific pests such as ants, dust mites, cockroaches, mosquitoes and flies.