This is probably a little more than you're looking for right now, but I think all of this will be useful.
Review the laws in your area regarding the application of pesticides, fungicides, herbicides, and fertilizers. Also review the availability for low cost/free courses on irrigation systems. Here in FL, The Department of Agriculture and Consumer Services require yearly licensing for the handling/application of most of the chemicals outside of a basic fertilizer.
Florida also restricts the application of nitrogen on turf from 05/31 to 10/01, it would be a good idea to review the same laws that might apply in N. Carolina.
Treating chinch bugs, fungus, grubs, ant hills, mole crickets, etc. and being able to adjust/fix/replace sprinkler heads are great add-ons for you, keep your name in the customers face, aren't difficult or time consuming, and are an added convenience for your client. Generating a good relationship will increases your work-of-mouth from your current clients.
Most of the necessary chemicals can be mixed in the same applicator in the appropriate amounts for both broadcast and spot treatments.
Site One here in Melbourne offer courses on the basics of most lawn/turf care stuff. Home Depot regularly has small, free classes to cover DIY basics as well.
If you don't want to provide anything beyond mowing, weeding, trimming, start making friends with local companies that provide the services that you don't, and don't provide the services you do. You can easily refer people to them, and they can refer customers to you.
Join any/all local Business Owner Organizations to rub elbows and build a social presence.
Get cozy with local landscapers that aren't currently offering turf maintenance so when their client needs a referral, they remember you. Half a dozen donuts when you stop in to buy a necessary thing can go a long way to ensure a good impression.
Schmooze HOA Boards and offer some meaty discounts for groups of lawns on the same block/neighborhood. I've sold plenty of 3-4 houses in a row by simply telling the person who called for an estimate that I'd happily discount it if I picked up any more accounts in the area. They'll usually talk to their neighbors and do some of the legwork for me.
Consider dropping some dough for targeted advertising as soon as you can. Take aim at one of the national lawn care companies in your area, offer to meet/beat their current price, and play up the whole "locally owned/operated money stays in the community" angle.
Don't be afraid to tell a customer that you're in over your head for a particular service. While I will happily adjust/replace sprinkler heads to ensure proper coverage and saturation, I don't even think twice to tell someone that they'll need to contact a company that specializes in irrigation system installation or repair to fix a larger issue. They'll appreciate the honesty, and trust you more when you say that "X" is wrong, and "Y" will fix it.
Last, and this one is a big one around here: Have a clean, professional uniform, and keep your truck/trailer in the best visual state as possible. A clean truck, with a professional looking crew goes way farther than it probably should. No one wants the neighbors in their million + neighborhood to think they can only afford a service in a dirty, old beater that smokes and squeaks when it stops.
I work for a pest control company and deal in turf maintenance on the daily with almost 400 accounts.