I think for 350 your better off finding a complete 'fixer upper' and then overhauling it rather a complete build, especially if your mechanical experience is limited. that will keep you from making common newbee mistakes like incorrect brake reach and wrong BB threading.

There are lots of here who spend way too much of our employers time looking for good deals on used bikes. if we knew about where you live somone may be able to point you to a good deal. Or even better maybe someone has one of the 15+ bikes waiting for rework they would make a good deal on.