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Here is a picture of a chart I made for drivetrain layout and engine options for my BB6.
Budget limited, I'd say staying front engine/fwd would be ideal with either a turbo H22A4 or a N/A J35A8.
I like the idea of front engine, rwd most, with either a turbo J35A8 or the LS7 or Ferrari F133E.
Next to that I'd say the best option would be a mid engine setup with either the turbo or supercharged J35A8 or maybe a LS7 or Ferrari F133E (transmission dependent)
My top choices in order of how ideal they are in terms of $-to-fun are: