Is it better to pick tomatoes early and allow them to ripen off the vine?

It depends on the variety of tomato. The seed pack gives you the days to maturity. This assumes that the plant has grown in a pot for 8 weeks prior to being planted. A seed pack that says 68 days to maturity would then take 89 days (including 7 days to germinate and 8 weeks to grow before planting in the garden). Then, that will be when the first individuals mature. Most tomatoes will produce a lot of fruit a little bit at a time until they die back.