What is the best budget LS build?

The cheapest big gains, in order (Speedway Motors 5.3 recipes):

1. Bolt-ons: cold-air intake, larger throttle body, headers.
2. Cam swap: a BTR Truck Norris-style cam on a junkyard 5.3 is about 400–430 hp. Delete AFM first on Gen IV engines.
3. Nitrous: a plate kit to about 500–600 hp on a stock-cam or cammed 5.3.
4. Turbo: a single turbo kit to about 600 hp on a junkyard 5.3.

For a 6.0 (iron LQ4/LQ9), Speedway's recipes run from a 500 hp cam + intake build to 800 hp with a single turbo on the stock bottom end (E85 required at that level). Budget for fuel system upgrades past ~450 hp.