First, does the distribution you want to use support 68LC040 processors? Have you done a search for known working installations?
I have a PowerBook Duo 280 and was considering Linux or BSD, but found that they didn't support the 68LC040 or the video in my system. My system isn't that different for yours, and I would think the lack of FPU would make it harder to find an OS that worked.
If I could have, I would have install A/UX on that system. It is amazing how important the FPU part of the 68040 is.