I'm unsure about this terminology. Is outgoing connection for me to get new block information from other nodes and is incoming connection for me to broadcast my own transactions out there if I were to use my full node with my hardware wallet?
Incoming connection means other peer/node which connected to your node, whereas outgoing connection is the opposite. As @ranochigo said, the connection is bidirectional which means your node can do every task without incoming connection.
You definitely don't need incoming peers to use Bitcoin. If you're behind a NAT, you have to port forward your port 8333.
Alternatively you could add
upnp=1 to
bitcoin.conf if your modem support and enable UPnP (Universal Play and Plug).