Don't know your budget, but my version of cheap is $1000 or less, so if you go with a 4" crank, pistons would be required, and a basic stroker kit would run you $1500+. Then cost of machine work if needed for an overbore. You could find a 360 from a wrecking yard for $350 or cheaper, freshen it up with rings, bearings, gaskets, to bring you to $500. You would also need a 360 torque converter because the balance is different, so $50-$350 depending on what you want, stock from wrecking yard or basic aftermarket.

If you wanted to stay with the 318, 1992-newer magnum heads can gain you 50hp just by bolting them on, but require a different intake, shorter pushrods, newer style lifters (great time for a mild cam kit, 260-280 degree range, about .470 lift) and 10 bolt valvecovers (which wont look stock.) The magnum valvetrain has an increased rocker ratio of 1.6:1, which turns a .474" lift cam into .506, which is about the max the stock magnum springs can handle anyway. These heads are a closed chamber design, which would raise a stock compression ratio of about 8.2 to 8.8, or somewhere close to that.

Have Fun!!
JJ


Edit: 1971 318s had higher compression to start with, 9.0 I think, so the end result may be 9.5-9.7, and the higher compression pistons may be close to hitting the valves in the .510" neighborhood, don't know for sure. And don't bother putting 360 heads on the 318. They do flow better, but have bigger combustion chambers, which will lower the compression ratio, nearly cancelling out any improvements from increased flow.