In this case, I'm betting there will generally be enough ambient light to see where I'm going well enough. I ride on a paved bike path that follows a significant road, then follows a waterway, then I pop on to downtown surface streets. I'm not sure about the portion of the path along the waterway, but I'm betting there will be enough light for me to not run into things or go off the path. I'm pretty sure I won't be riding down an unlit country road.
Any specific product recommendations in light of this?
There are so many options, I can understand why you're asking for recommendations. I don't have one. Here's what to look for in cheap lights:
Efficency - eliminate any that are not LED based.
Brightness - is it bright enough over the field that you care about?
Mounting options - Some are easy to mount, others are a pain. Most headlight are easy enough to mount on most handle bars, but sometimes the handle bar is too small/large in diameter for a particular light. Many rear lights mount to the seatpost, but does that work for any loads you might carry on a rack? Most lights feature a quick release mount - if this is important to you make sure.
Modes - less is more: The cheap lights all seem to be controlled by one button. Many of the headlights have a dim, bright, and flashing mode(s). Many of the tailights have a solid on and multiple flashing modes. This means to turn the light on/off requires multiple presses of the button - so although the marketers love many modes, I do not.
I did like MMM's article about the lights he chose. The bottom end of the market is filled with way too many options that you probalby would find suitable, yet they are priced low enough that the effort to compare them does not yeild much reward. I've never bothered to do more that shop for the cheapest item that meets my needs at one or two stores (most often nashbar and/or amazon and a physical store if shipping time/costs are a factor).