To stroke or not to stroke......

Hmmm....Big choice to make. I'm thinking of swapping my 318 for a 360 in my 68 barracuda. Well, I've been kicking around the internet and I haven't found the answer to my questions.
I want a STRONG street/strip engine. I use my Cuda only in the summer months as a dd. (garage in winter) And I race a couple of times a month.
I haven't read anything on building a hot 360 or going for a stroker. Which will give me more at the track? And will it be driveable on the street as well? What are the pros and cons? And have any of you built a stroker?
My buddy(an engine instructor at a near by univ) plan on building the engine over the winter so I want to get a head start. And my budget is high enough for pretty much anything.
Please, any imput would be great. And I don't want a crate motor. We want to do it ourselfs.