b'Twin Bottom Bracket

As for the spokes, in case you haven't done so already, go for the widest tires you can, adjusting the pressure exactly to your weight needs. Wider tires will take some stress off the spokes.

I'm 'only' 78kg and have broken 3 spokes this year. 2 on a handbuilt set of dura ace/archetype/Sapim race wheels and the other on Giant PSL1 wheel! Been told to try putting less air in so now using 100psi. Also had the rear wheel relaced with CX ray which are stronger. You may need some heavier wheels, better rims and more spokes.

Looking at the Shimano specs for the Claris Triple (FC-2403) Octalink Crankset it says 121mm for the Bottom Bracket  spindle length, which gives a chain-line of 45 mm. You are correct in assuming the 68 mm shell size is what you require; that is the standard ISO / “English” size of  bottom bracket shell, 73 mm is “Italian” size. So you want either a BB-ES25 x 121 mm (which is almost certainly what is currently fitted to your bike) or better quality is BB-ES51 x 121 mm.

As for your spoke breaking issue, as you say that will be down to the weight they have to carry. I don’t think a suspension seat post will make any difference, as the total weight is still on the wheels.   Not sure how many spokes your wheels have, but going to 36 spokes will help a lot, as the weight will be distributed over more spokes, so less stress on each individual spoke. You mention double butted spokes they will also help a bit.  As they are thinner in the middle  of their length they bend more than straight gauge spokes when absorbing the force of impacts, resulting in less impact stress / fatigue at the J bends where spokes break.  

Another issue is the spokes might not be tensioned high enough and uneven tension on the spokes around the wheel. If the spokes aren't all at the same tension (give or take) some will have more stress on impacts, so fatigue / break quicker. Also if the wheels are "machine built" the spokes won’t have been properly “stress relieved”.  

If you aren't doing so already, when you replace the spokes lubricate the inside of the eyelets in the rim and the spoke thread with linseed oil ,that will help them turn more easily to achieve the correct (high) tension.  Also the linseed oil will harden acting as a sort of thread lock to stop them loosening. You then need to go around the wheel checking all the spokes are about the same tension, as you get the wheel "true" (obviously on a dished rear wheel the non drive side tension is less than the drive side and similar on a front wheel with disc brakes); that can be done by plucking each spoke and listerning to the pitch of the sound it makes or a more expensive option is to buy a tension meter. I get by using the sound each spoke makes. As for “stress reliving” that involves squeezing pairs of spokes together. If you haven’t read it, a very good book available to download for a small fee that is well worth paying is “Guide to Wheel Building” by Roger Musson. The tensioning / truing steps you need to do when you are replacing a spoke is exactly the same as if you are building the wheel from scratch.  Following the guide I've never had a problem with trueness or broken spokes on the wheels i have built  on pot hole covered roads or even when my touring bike is "loaded up" and going over some of Sustran's delightful paths / trails.