1GHz and lower than 100$us??? and you don't like the raspberry pi? I think the new raspberry pi 2 with it's quad core ARM SoC should be enough.
+ it's cheap, very cheap! 35$us
+ ARM Cortex-A7 processor (32 bit) quad core at 900Mhz that you can overclock(careful there) has USB and ethernet (and SPi usart, and general io) you can buy 'shields' and expantion boards ala arduino
+ you can make your own ide with existing tools, like ECLIPSE and a GCC cross-compiler which are free...
+ if you don't like to program within an Linux OS you can try a
"Bare Metal" approach (that one use IAr but i think you can look on the internet for a GCC solution)
+ it has a JTAG port somewhere (
this is for a Pi 1 but more googling could fall for a Pi2)
+ some googling and it seems there are
FreeRtos port for the Pi, some legwork and you can get one for the pi 2
+ a lot of communities, no only for OS distributions, but also for hardware and the BareMetal stuff...
what exactly do you want to do? for that speed and a simpler device than a pi, maybe you should look for a ASIC or something similar...