Let me start by saying that I agree the RIGHT way to do it is to tear the motor apart and have it cleaned and inspected.
A complete rebuild will be expensive. If youre working on a tight budget, like I have many times before, Id go about it another way.
Id browse the local classified papers or talk to friends or neighbors and start looking for another 350. Theyre everywhere, rusty old pickups, '70s and some '80s passenger cars, grandpas barn.
Then Id get a re-ring kit, can be had for under $200 and usually includes rings, bearings, and gaskets. Buy a $30 hone, slap the rings and bearings in, get a NEW oil pump, carefully clean and inspect your old camshaft, replace the lifters, and bolt on the intake. Youll be down the road for around $400.