Well, the only way to find out if 350 is too low, is to make the offer and see what the seller says!
it doesn't really matter what anyone here thinks......and really, no one here can have an opinion on a house they know nothing about!
It sounds as though you are not working with an agent - otherwise, they could give you a sense of market conditions and recent closed sales. Armed with that information - YOU, yourself, could make an informed decision on this home's value.
When all is said and done...... you are the best judge as to what the house is worth (to you)......along with the appraiser when the time comes!
Best wishes......have a continued happy holiday season!