I'm looking into a small inexpensive irrigation solution. I'm looking at buying 300' of drip tape and a few fittings. My rows are 300 ft long and generally have a different crop in each row. I figure I can just start with one line of drip tape and move it. Do people think this is a good solution?

I have city water and some small ponds. I'll probably use city water for now. My ponds are brand new and not full yet. Last year I irrigated not at all and some things like tomatoes still grew ok. Supposedly my region gets about 40" or rainfall in the average year, but last year I watched all the scattered showers blow 10 miles to the north of me and it got really dry.

You probably had problems with bolting and not water if you tomatoes did 'slightly okay'.
Because tomatoes are resource/water heavy monsters. Your spinach and cabbage family crops should already be in the ground, in your zone 6b and out of the ground by june, followed by some summer crops.

To answer your question about moving the drip tape, I'd say to avoid it. Drip tape isn't particularly rugged and 300' strip will be a hassle. Of course, it will depend on how many rows your are irrigating and how regularly. In the end, if you do decide you want to move it a lot, I would highly recommend building yourself some sort of drip tape rolling/winding tool. It will make the whole process much quicker. Here are some good pictures of a winder:

http://www.joshvolk.com/photojournals/Drip%20Winders/