Make certain the work is done well and is competitively priced. A good handyman can make you a better landlord. Pest control is the landlord's responsibility. Shop around for the best combination of service and price. If there is a pest problem due to unsanitary conditions caused by a tenant, you have the right to demand that they clean up or otherwise correct the unsanitary condition.
Conclusion Always start with good tenants.
Use common sense and good judgment to avoid future, costly problems.