Does the $350 budget supposed to include everything?
You know the mic, radio, coax, antenna, etc?
If just the radio; I would get a President Madison (4th generation -~$300), Cobra 2000 GTL (~$300), Cobra 142 GTL(~$200), or a CPI 2000 (~$300).
If an export; then a RCI 2980 or an RCI 2990 (either ~$325).
Personally, I prefer to use a 'export' 10 meter mobile radio with a 12v supply.
Like a Magnum or a Galaxy...