Best preamp (used or new) under $350???

If you want strictly a 2-channel preamp, you are probably looking at some sort of really old NAD or Adcom.  However, if you look at the bargain basement home theater processors, you can get a real gem.  The HT Processors really don't keep their value at all because of the perception that you need the latest and greatest digital decoding / HDMI2.0 / Atmos, room correction, etc. etc.  As a result, the value drops like crazy the older they get (this is not like 2-channel audio!!!)  The older HT processors can be used as an extraordinary preamp for the money.

On Audiogon, there's a used Krell Showcase for $200.  There's also a Rotel RSX-1058 for $325.  The Rotel is newer, of course, so the long term reliability may be a lot better and it supports a lot of new formats (HDMI).  However, the Krell processor uses their fully discrete Class A analog circuits and also has balanced XLR outputs.  You would probably need to hook these up to a television/panel to configure it, but once it's configured, all you need is the remote to adjust source and volume.

You can also use these as DACs that can actually be superior to many other 2-channel DACs. 

I used a Krell HTS 7.1 for 15 years before it finally died.  It beat the crap out of several other items that I tested and I continued to keep it even though it did not support newer digital formats.  The Krell was limited to digital coax (which means old school compressed Dolby Digital and DTS), but it still sounded better than the hi-res bluray audio through an Emotiva processor -- proving that the newer hi-res formats are not necessarily a silver bullet.