Joshzilla,
once you get rolling it will all become clear. You can post and read lots of messages but it doesnt come close to what you would learn in one weekend of battling.
But the quick down and dirty...in Laymans terms ( I am leaving off many details.. this is not wikipedia)
C is used to describe the battery current output. 1C = the capacity of the battery. So a 12ah battery 1C=12ah. Simple. SLA batteries, if I am right, have a low output. I was told 1C but I don't think that is true.
C is also used to determine the charging current. My battery manufacturer wants the cells charged at 1/3 C so my 20ah cells should charge at a rate of 6.7 amps. They can output up to 3C so 60amps of output.
Amps is the measurement of current, aka the load. The 'C' determines the max current flow through the battery, expressed in amps. So if you have use my cells as an example, with 3C output, and my motors draw 12amps and my pump ran at 30amps for 1 hour straight it would take approx: 42amps of the 60amps output capacity (3C) and it would take approx. 1/2 hour to completely drain my 20ah batterys (42amps per hour/ 2 = 21amp hours per half hour). Of course this usage scenario never happens but is listed just as an example.. its easy math.
Amp hours is the energy stored in the battery expressed as amps/hours. Basically it means that a 12ah battery can supply 12amps for 1 hours... 12 individual amp hours... So if you are pulling 4 amps.. then you can go for 3 hours (12ah/4amps).
So for battery capacity planning.. you can figure your motors and the approximate time you would be using. At the recent Brouhaha I used 9ah of 20ah in my most damaged sortie and I pumped full stream for 10-15 minutes max (standard BC motor at 10.2V... I have no idea what amps it was pulling), with me driving around most of the 20 minutes I am on the water.
In my limited experience (3-4 years) I have found that at a competitive event.. the veterans might be on the water to the end but generally most noobs will be on 15-20 minutes max unless the veterans are being nice to you.. which they did for me at my first few events... unless I started something... which I did.

And sinking is no big deal really... its part of the game...you have to make it part of the fun also....(unless its a mechanical failure then its a bit frustrating)
If I had a slow pump I would be on the water even less time per sortie... I want max time on the water!!!!
I run a separate receiver pack so that my guns will always fire in the event of any type of main battery problem (failed cell, broken connector, etc.) I bought some 3ah life cells, F Size I think, and they work great. I charge them with my Hyperion charger (life, lipo, nimh, SLA). You can also buy a pre-built pack from just about anywhere that is a 5 cell 6v pack and just put a deans plug on the end of it. I have used the packs from Tower but they were so expensive I made the Life receiver packs.
Hope this helps you out...