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Generally speaking, the higher rating amp hour deep cycles will have enough oomph to turn over moderate draw engines on start; that said, if it gets really cold where you are, you could always build a jump box like what I have for jump starting other vehicles since my car basically has a motorcycle battery in it and can't really handle that task too well on it's own.
The only time I think you'll need a hybrid setup with lead acid and caps is if your lead acid system isn't capable of running your highest short term load (starting the car) most of the time, but is properly sized for your long term low drain loads. In that case, you should endeavor to figure out how much your engine requires to start, and try to build a bank that has a farad rating of Amps / 2 (assuming no current limiting from battery to cap bank).
If I were in your situation, and since I know my car requires 500 amps to start, I would design a bank that has a farad rating of no less than 500 / 2 or 250 farads; this way I know my system voltage won't drop below 13.8 - 2 = 11.8 volts during start, thus minimizing the drain to the battery as much as possible without having a massive cap bank taking up space as well.
I have a couple ideas on a higher voltage cap bank setup (14) with a lower voltage battery setup (12.8) where the cap bank is smaller and isolated from the battery until start, but I really have no way to know if it will work or is even possible.
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