So now the search for a decently built rifle for around 300 bux in whatever caliber, new or used.
For $300 it's definitely going to be used.
For $400 you can get into some better rifles.
If all you really have to spend is $300 then look at the Marlin XL7. Seems to be a decent rifle for the money and generally plenty accurate.
Your buddy couldn't be more wrong about the .270 Winchester. It is one of the absolute best all around cartridges ever devised. The only cartridge I would recommend above it would be the 30-06 if you are only going to have one rifle/cartridge.