Ardunios are fun. I almost always have 4 or 5 on the work bench. Though recently I have found myself moving towards single board computers. The PI zero costs about the same as an Arduino dev board and is orders of magnitude more powerful.
I'm currently working on a remote telemetry project using these cool little Arduinos
https://www.adafruit.com/product/3078#tutorials. They have wifi, Bluetooth, and LoRa radio built in.
Blinky light is always the first project.
For beginning I recommend
LED clock
LED sign
NeoPixel or WS2811 art
Line following robot
Mini Sumo robots
Robot arm
I've done really advance projects with them for automation and control. However my favorite is coke bottle lights. I took 15 glass coke bottles and stuffed three 12 mm LED WS2811 LEDs in each. The WS2811 led are three color leds you can control hue, intensity, and saturation on. I wired them all in a string and programmed an Arduino to make them do patterns and effects. They are hanging on my porch. When ever people come over they get a kick out of them.
Once your son gets advanced building you own quad copter and teaching it to hover is a lot of fun. However that is really not a beginner project.
For a beginner, beware of knock off boards. Chinese knock offs abound on eBay and Amazon. Arduino boards are pretty basic and most of the time Chinese Arduinos are acceptable. However, they have a high failure rate and they normally don't have a real FTDI chip for programming. When you are starting out messing with defective chips is a good way to get turned of to them. Spend the $20 bucks and get a real Arduino from the foundation. It also supports a good cause. Once you are proficient, buy the knock off for 1/4 of the price and throw away the ones that don't work.