What will be the easiest/cheapest way to get lower gearings on my "new to me" road bike?
You seem to have a good handle on your options.
A wider-range cassette, and a derailleur with a long cage, will probably give you the most bang for your buck. Switching from a 39t small ring to a 34t small ring is comparable to switching out your 25t big sprocket in back for a 29t sprocket. This is a good tool for playing around with gear ratios.
If you do go with option 4, you have more options. I recently built up a new bike with 46/30 in front and 11-30 in back. This gives a high enough top gear for me (46x11 is plenty fast for the kind of riding I do), and a 1:1 ratio at the low end, with tight spacing in between. Shimano, FSA, and some of the more exotic brands offer cranks with 46/30 chainrings.