cheapest way to 300

[84LX89GT]

You want 300 hp on tap, and more with a simple swap.....get a SUPERCHARGER
For overall cost in the longrun and convenience of not having to get a bottle, i believe it would be best to get a supercharger. A vortech A trim, or powerdyne are usually advertised at under $2000 for a kit to start with (small HP kits, but will easily get you to 300 hp).
Building your engine may be not worth your time because of mileage or other reasons, plus it takes alot more time to build your engine right than it does to put on a supercharger kit.
A nitrous kit is the simplest solution and cheapest, but inconvenient because of refills.
300 horsepower is running just a little below the point where you'd have to start upgrading your fuel/ignition/suspension, etc. etc. etc. to deal with the extra power and torque, so that's probably a good number to go with. You may want to invest in subframe connectors and rear control arms to go with this stuff just because it makes driving your car better overall.
Good luck,