Since I have some experience with which connections are usually made and not usually made, I would carefully pick and choose which ones I would chance and those not to chance. For example, I would book a same day connection from the Southwest Chief to the Starlight at Los Angeles, but not from the Sunset Limited to the Starlight since I know that one is usually not made (although the last six of these have actually connected, impressively enough).
Finally, even though I do tend to worry a little about making connections, I have learned it is better not to and to just accept whatever happens as an adventure, go with it, and ultimately try to make the best of it. Have fun! B)