The $3000 mark is a bit low for a new block, crank, pistons, rods, cam and heads. A stroker kit would be the best bet for a non fussy engine that has the kind of power you want. A 351 will make an easy 350 flywheel HP, but 350 rear wheel HP is going to take some extra effort. There is roughly 20% losss in the drive train, and more with an auto trans. That means 420 flywheel HP to get your 350 rear wheel HP. Cranking that kind of naturally aspirated power out of 351 cubic inches can be done but the engine is not so street friendly as a stroker would be.
For a $3000, 350 RWHP, you would need a used supercharger and used heads and a good dyno tune to meet your goal on a 302-306 engine.