How many affordable lithium polymer batteries would it take to safely jump-start a car

Measure open-circuit voltage \$V_{oc}\$, then load the battery with resistor \$R_{load}\$ and measure voltage \$V_{loaded}\$.

$$ R_{in} = R_{load} \cdot \frac{V_{oc}-V_{loaded}}{V_{loaded}} $$

This is the internal resistance at DC and at your specified load. Internal resistance varies with load and temperature and battery charge and age, etc. And you'll need more advanced equipment to measure at higher frequencies.

Among mainstream battery technologies, LiPo has the best energy density, so you will probably want to go this way. In your case, since you will use a regulator anyway, every configuration possible (including single cell combined with a step-up boost regulator). Once you have chosen the total energy capacity you need for your application and the cell configuration, there are two parameters to consider:

1. Quality: for the best specific energy, you will need to get high quality cells, which are going to cost more.
2. Discharge rating: cells are usually rated for a given maximum discharge current, usually expressed relatively to its capacity (for example, a 10C rating for a 1000mAh cell means that the max current is 10*1000mA = 10A). While higher C rating may mean a lower ESR, there is a trade-off and increasing C rating significantly lowers the specific energy. As an example, a 40C 2000mAh cell from a high quality chinese manufacturer I was looking at recently had a specific energy of about 140 Wh/kg while the 15C version had a specific energy of 170 Wh/kg. This difference can largely offset any loss due to slightly increased ESR.

Whatever configuration you will end up using, your require that the battery lasts at least 5h. Assuming little loss in DC-DC regulation, this means that the average current would be at most 0.2C and the peak current (from your numbers) about 0.6-1C. I would thus look for 5C-rated good-quality cells, which should get you 180Wh/kg or more.