You can get ethernet ADSL modems with a single ethernet port (for one user) or one's with additional ports.
Ethernet modems cost more than USB one.
The reason your modem is acting odd during start up is a mystery, but remember that the USB ports power up after the computer starts, whereas a ethernet modem usually has it's own power supply, so is on all the time it's plugged in, and isn't depended on the computer for power.