350’ is the same as 151 PSI. So I would just use 160# poly all the way to the pump. You can get a splice kit with heat shrinks and butt splice connectors at many stores. I like the thhn/thwn, double jacketed, round cable. It is made for direct burial and works just as good in the well. It is not NSF or rated for submergence, but I have run hundreds of thousands of feet of it in wells as deep as 2100’.