Almost all AT thru hikers just resupply along the way of course but it is possible to resupply via mail drops if that's your preference. Here's what I did. First I had a lovely wife who would fill my box with my backpacking food and then usually would use USPS priority mail boxes ($23 per large box, $17 per medium box) and mail them to me. It would usually take 3-4 days for it to arrive and she would follow the instructions of the place she was sending it to and send it so it arrived a few days before I arrived (sometimes a hostel, sometimes just post office general delivery). I had the addresses and what I wanted all written out for her and then just communicated with her if I wanted to change anything up.

At first each box had 5 days of food but then after I switched to my cold weather gear I could only really easily fit 3 days of food in my backpack. A typical 5 day box would have:
4 granolas (3/4 granola and 3T of dry milk) (on trail I'd add my instant coffee to it and cold water and it was my favorite breakfast)
1 either MH eggs breakfast or 2 packets of instant oatmeal (just to mix things up)
4 packets of instant coffee
1 instant refried beans and instant rice dinner (a cup of each, just add hot water and easy to make and my favorite backpacking dinner)
1 stuffing, craisons and chicken pouch dinner
1 mashed potatoes with dry milk, garlic powder, minced onion and pepper and a pouch of bacon
1-2 other dinners (examples: chilimac, ramen tuna noodler, couscous with taco seasoning and a chicken pouch, a mountain house dinner etc.)
and various snack items to fill in the box (electrolyte packets, raisons, banana chips, peanuts, pistachios, clif bars, trail mix, smart bowl tuna packets and a couple of tortillas, candy etc.)
(I found it easy to buy snacks along the way but was very happy to have my breakfasts and dinners taken care of so I wouldn't worry if I needed to supplement snacks)
6-7 pills of the medicine I take, 6-7 vitamins
5 wet wipe packets (I used one every night in my tent to clean up)
anything else that I was running low on (tiny toothpaste, hand sanitizer, occasionally a disposable razor or a couple of qtips etc.)
This worked for me, obviously you do you!

Here are the places that I used to resupply via mail drops. Please please call or check to confirm they are still open and accepting mail drops before you send. I never had to pay for picking up my box but I was always super polite and tried to stay at or purchase something from where I was picking up (assuming it wasn't a post office general delivery of course). I'll go from north to south even though I was a flip flopper.

Mile 31 NEELS GAP
Mountain Crossings, 12471 Gainesville Hwy, Blairsville, GA 30512

Mile 136 NOC
Nantahala Outdoor Center, 13077 US 19W, Bryson City, NC 28718

Mile 164 Fontana
Fontana Lodge, 300 Woods Road, Fontana Dam, NC 28733

(Great Smoky Mountains National Park - didn't go into Gatlinburg but you could of course and that might change the places you send to)

Mile 241 Standing Bear but I think if I were to do it again I would try a different spot here, maybe the Discerning Hiker Hostel

Mile 275 Hot Springs
c/o General Delivery, 111 Bridge Street, Hot Springs, NC 28743

Mile 344 Erwin
Uncle Johnny's Nolichucky Hostel, 151 River Road, Erwin, TN 37650 (my wife actually visited me in Erwin so I didn't actually send a box here)

Mile 470 Damascus, VA (originally was going to do general delivery but switched to where I was staying instead ie Dancing Bear, there are also lots of hostels here in town too)

Mile 546 Rural Retreat, VA (originally was going to do Quarter Way Inn in Ceres, VA mile 555 but they were closed for the season when I went thru, loved the Alpaca Farm)
Long Neck Lair Alpaca Farm, 7530 Lee Highway, Rural Retreat, VA 24368

Mile 625 Pearisburg, VA
Woods Hole Hostel, 3696 Sugar Run Road, Pearisburg, VA 24134

Mile 730 Daleville or Troutville, VA (I used Beech Hill B&B and they were very nice but I might use the Super8 if I were to go again - both very close to the trail)

Mile 864 Waynesboro, VA (so nice here that post office lets you ring a doorbell and get your package on Saturday if a worker is present)
c/o General Delivery, 200 S. Wayne Ave, Waynesboro, VA 22980-9998

Mile 972 Front Royal, VA or mile 1019 Harpers Ferry (I was a flip flopper so didn't send a resupply to either of these spots as I had enough food on me)

Mile 1067 Cascade, MD
Zero Day Stay Hostel, 14530 Maryland Ave, Cascade, MD 21719

Mile 1124 Boiling Springs, PA
c/o General Delivery, 3 E 1st St., Boiling Springs, PA 17007-9998

Mile 1219 Port Clinton, PA
c/o General Delivery, 6 Broad St., Port Clinton, PA 19549-9800

Mile 1296 Delaware Water Gap, PA (my wife picked me up near here so sklpped this resupply point too)

Mile 1338 High Point, NJ (again very nice here and even offered to put my box in the area that remains open if I wasn't going to make it by closing time)
High Point State Park HQ, 1480 State route 23, Sussex, NJ 07461

Mile 1406 Bear Mountain State Park or Mile 1425 Clarence Fahnestock State Park (my hiking partner had a good friend meeting us in this area so I just mailed our box to her)
Mile 1451 Native Landscapes and Garden Center, NY (see above, didn't send a resupply box here but they seemed very friendly)

Mile 1496 Falls Village, CT
c/o General Delivery, 5 Miner St., Falls Village, CT 06031

Mile 1580 Chesire, MA
c/o General Delivery, 214 Church St, Cheshire, MA 01225-9998

Mile 1705 Inn at Long Trail (they require UPS or FedEx, read instructions on their website)
Inn at Long Trail, 709 US Rte 4, Killington, VT 05751

Mile 1794 Glencliff, NH (read instructions, different address depending on who is delivering the box)
Hiker Welcome Hostel, PO Box 25, Glencliff, NH 03238

Mile 1874 Pinkham Notch (triple check this one, it made me nervous but it did work for me to send a small box here and I was able to get over the Wildcats and Carters)
AMC Visitor Center, PO Box 298 Gorham, NH 03581

Mile 1894 Gorham, NH
c/o General Delivery, 165 Main St, Gorham, NH 03581-9998

Mile 1972 Rangeley, ME
c/o General Delivery, 2517 Main St, Rangeley, ME 04970-9998

Mile 2070 Monson, ME (sent myself more breakfasts and dinners here so I could use Shaw's resupply service to get thru 100 mile wilderness)
c/o General Delivery, 2 Greenville Rd, Monson, ME 04464-9998

I tried to pick places I would be walking by or visiting anyway (besides Fontana Dam, Waynesboro, and the last 3, I walked to each pick up spot). I knew from hiking the Long Trail and backpacking the NH 48 basically what my mileage would be and so I knew how much food to send myself and what I liked (I was proud of the fact I would often have it so dialed in I would comfortably walk into town with very little spare food). On the rare occasion I would arrive in a town with say an extra dinner - no worries, I would eat my backpacking dinner as my first dinner before buying a second dinner in town. In this way and by the fact that my wife would buy the granola, instant beans, instance rice, dry milk etc. in bulk - I do think it was a cost effective way to go for me. Every hiker is different though and this is certainly more work for your loved one at home. I'm only sharing what worked for me to try to be helpful, please do what works for you.