As far as flattening goes, you can start yourself off flattening for cheap with sandpaper, but as time goes, it turns out to be the expensive alternative as sandpaper wears fast and the cost will accumulate. In the long run its actually the expensive alternative and the messiest one to boot. If you are willing to take a instant hit to the wallet and get it over with for a while, DMT Diasharp plates do the job well. however, for very coarse stones (500 grit and below) I recommend sand paper as the coarse stones are not likely to be used often ( unless you chip your edges constantly or restore a lot of old tools) and the coarse stones will wear out the diamond lapping plate fast. The Shapton diamond flattening stone is probably the best one out there but is very costly. Being so costly, it is suggested you use it only to flatten stones 4000 grit and above to avoid premature wear, unless of course you don't mind spending 3XX$.
If you want something in between the price of DMT and Shapton, there are the Atoma diamond lapping plates. They are around 100 dollars and the guys on the shaving razor message boards say they are flatter than the DMT diasharps and have the diamonds arranged in patterns so that there is no suction to the stone being flattened. You must apply pressure evenly and carefully while lapping if you use a diamond lapping stone more-so than a larger surface ala sandpaper on a reference. In the past, I have experienced what David has mentioned by lapping fast and heavy handed and without much thought.