This is a very specific question. We're from all over the country on this site. But here are some basics:
Having a catered party means considering several things: your budget, your kitchen/yard/grill situation, dietary concerns (allergies), food preferences (for example, your son hates seafood but loves burgers, or wants BBQ, etc), the theme of the party (formal, informal, picnic, Star Wars, etc), the age range of the guests (teens and parents, teens and young children, just teens, just adults, etc), drink preferences (adult beverages properly supervised, or no alcohol at all, etc), and then time range of the party (from 2-6, or 7-10, for example). You'll also need to consider if you want lunch served when everyone is seated at the same time, or if you want a constant buffet going on. You need to decide if you're providing a birthday cake or if you expect the caterer to arrange for that. You need to decide if you want the cooking done at your home or if you expect the caterer to deliver hot food or food ready to serve (this depends on the size of your stove, the prep area, etc).
Ask to see the caterer's license, food handler's certificate, insurance, and ask for references. Then call those references. Ask if the caterer was prompt, sanitary, polite, agreeable, and how the food tasted. Ask how dietary concerns were addressed (with respect, or with subtlety, or with scorn).
Ask what dietary issues the caterer can address (how do they deal with gluten-free, dairy-free, vegan, etc? Some caterers do not have a gluten-free option or other allergen-free menu items, or some need an exact count of the allergic guests and what allergies there are, and others have a wide range of food choices available for guest with allergies or religious or dietary restrictions).
Ask the caterer what they require of you. Who does the clean-up? What basic items do you supply (oils, sugar, salt, spices, etc)? Do they allow guests or the homeowner in the kitchen while they're cooking? What about plates, napkins, cups, flatware, serving ware? What time frame does the caterer require (how far in advance do they come to your home, do they need to come a few days before the party to look things over, etc)? Does the caterer serve the food, or bring prep cooks or servers or bartenders? Or do you do the serving and the caterer only does the cooking?
It would be better if you look at Yelp under caterers in your city. Or visit a couple of caterers and interview them. Bring photos of your cooking space and supplies, where the party will be held (backyard, indoors, etc), and your food preferences and allergy concerns.
But I hope those things I listed will give you some things to consider when choosing a caterer. I have worked for a caterer and these are many of the questions to consider.