I have consulted Tablepress and have done some experiments using Supercache.
It seems that there is a big conflict with using tablepress. The cache doesnt seem to get cleared, pagination doesnt work and load times are horrendous causing script error faults in Internet exlorer, Chrome and Opera. Firefox isn't so bad but some features do not work with the table.
The table is quite large and usually takes around 10 seconds to load. When SC is switched on this makes the page time out and filters , dropdowns, pagination of the table does not work.
The table is one table which is generated on several different pages but in various filtered states.