I thank you all for your advice and opinion.
Just in case you're wondering what my final choice is - I ended up purchasing TNG season 1 from Amazon, so it should come soon! It was a tough tie between The Next Generation and TOS, but after watching First Contact, and Patrick Stewart being one of my favorite actors, it only seemed natural. I'm aware the first season isn't the strongest, but I'm prepared!
I'd also like to check out DS9 sometime too.