Does anyone know what power the SP3 would need to charge and hopefully, be used at the same time?
Short answer: 31 W
Longer answer: The SP3 power adapter provides an output of 12V and 2.58A DC. That is the max power output from the power adapter to the SP3. Power is calculated by 12 V x 2.58 A = 30.96 W. I would round up to 31W.
In comparison, the current iPad is 12 W, and the current iPhone is 5 W. If you want to be able to power devices simultaneously, then you'll want to find out how much power other devices you would like to plug in would take. You might also want to add a safety factor ;-) For an SP3 and two phones, 50 W should be sufficient.
For myself, I would probably check how much power our laptop takes, and I probably would end up getting a 100W or 150W power inverter with multiple outlets. However, if I was getting one just for my SP3 with one outlet, I would probably go with 36+ W and compare prices. Actually, I would probably try the one I included the link to since I could plug my phone into it by USB, doesn't cost a lot, and has good reviews.