Beware the Bonetti. It is the same box as the Hohner Ariette. Both are made in China and are of extremely low quality. Their difficult playability only makes learning that much harder.
Your budget is a problem.
Look for a used Hohner HA-114 - they can be found for $350-$400 used, often higher. Gabbanelli Cajun Kings and Weltmeisters cost about twice that used. LA handmade accordions range from about $1200 up, averaging about $1800 used.
It might be wise to wait and save up for an instrument that will reward your time and effort.