350 hp is easy. Have a good stock rebuild done with these upgrades. Flat top Hyper-eutectic pistons, Moly rings, Double roller t-set, a good mid range power hydraulic cam, M55a oil pump, steel sleeve oil pump drive (for reliability).
Then you get to the heads. Have a good three angle valve job done, you will usually need guides, so go with the bronze, use premium seals and Z/28 or better valve springs, mill the heads .010.
Add a good Performer type intake, a set of headers and a 650-750 vac secondary carb and you will have a reliable powerful engine.
Shop wisely and don't get hung up on brand names, do as much labor as you (and some Knowledgeable buddies) can and you can do all this within a budget.