If you accept their version of the contract verbatim, chances are they haven't specified a maximum dollar value of your liabilities to them. Of course, it might still be a losing game for them to sue you into bankruptcy, but that doesn't mean they won't try.
I think that 'unlimited' personal liability needs to be put in perspective; I mean, you take the same risk every time you drive anywhere. Think of it; If you kill someone, and you very easily can when operating a motor vehicle, you can easily be liable for millions of dollars of civil damages. (not to mention the death of another human being.)
Yeah, you have insurance when you drive, but that only covers you up to a certain limit. you can get liability insurance for your business that does the same thing; and judging from the relative costs of those two types of insurance when I've gotten quotes, when you are small, you should probably worry a lot more about the liability you incur when you drive than the liability you incur when you sign a contract.