A new chainset would enable a more reasonable difference between a 24t inner and the middle ring, but there's no need for a new chainset otherwise.
Personally, I find a 39t middle ideal for cruising speeds and moderate hill climbing (with 13-29 and 14-30 cassettes), which is what I need for most of the time, so I stick with this despite it not being an ideal neighbour to the inner ring.
I recommend trying 26/39/50 first of all, then perhaps consider a new touring chainset with something like 24/36/48 if the bottom gear is still not low enough. I can't really recommend the 24/39/50 I have (on one bike) because of the very tricky setting up and awkward shifting to and from the inner.
[Edit in purple]