First solution - perfect match but expensive.
Asus prepared solution which is perfect for your requirements but it's really expensive and it's over your budget. It's ASUS CS-B:
It meets your requirements:
Dual LAN:
- Intel® I217LM
- Realtek® 8111G
USB Ports
- 2 x USB 3.0
- 4 x USB 2.0
It's mATX.
But:
Cost: $200 (Amazon US)
Second solution - better and cheaper
You should just use @john kieran solution.
