If you are recirculating constantly, you don't need to think about a "mash thickness". The grain bed will compact the same density no matter how much water is in the mash system. Mash thickness is a thing to consider if you are simply adding strike water to the grain and letting it sit static for the duration of the mashing (like in an igloo cooler). In a recirculating system, the grain sees a constant density. In theory its almost backwards, having more water on top of the grain during recirculation (or having a higher flow rate), actually compacts it slightly more, thereby making it "thicker". But in 5 to 10 gallon systems, its not a large enough factor to even think about.
That being said... You need enough water to keep flowing through the grain, allow for what the grain will absorb, and fill your tubing, pumps, herms coils, rims tube, false bottom area, and any amount of wort you want to always be on top of the grain bed.
In most recirculating systems, there is no "lost" wort or "dead space". Fresh sparge water comes in as the mash drains. The wort is being "exchanged" for water during the sparge. The fresh water comes in from the top as it slowly drains out of the bottom. At the end of the sparge, everything is left with fresh water (yes, there is always a tiny about of wort left). So, back to mash water...
Grain will absorb approximately 0.12 gallons of fluid, per pound of grain.
There is gaps between all the kernels and bits of grain that need to be filled.
A tiny bit of water will evaporate during the mash
So... Using a 1.25 quarts of water, per pound of grain, is a great starting point to make sure the gain is fully submerged and absorption is considered.
Consider the following example as a starting point for calculating the mash water needed (these are numbers from a batch I did yesterday)...
Total grain weight: 8.43 pounds
Water needed for the grains (1.25 quarts per pound X 9 pounds): 2.63 gallons (10.54 quarts)
Tubing, herms coil or rims tube, pump, valves, whatever: 0.5 gallons (you need to measure this in your own system)
Area under the false bottom: 0.25 gallons (your's would be 2.5 gallons)
How much water you want to maintain on top of the grain bed during recirculation: 1.25 gallons (you need to calculate this based on your kettle diameter. most people like about an inch and a half)
Therefore, total mash (strike) water is: 4.63 gallons
At the end of the mash, sparge until your preboil volume is reached. If for example your preboil volume is 7.36 gallons, you will need at least 3.73 gallons of sparge water. 7.36 - 4.63 = 1.7 PLUS the amount absorbed by the grain (1.01 gallons) = 3.73. Of course, give yourself an extra couple gallons extra sparge water.
Hope this helps