Very few of them will start a dead car IME. I once borrowed a small professional one from a garage when I got stranded with a completely flat battery. They didn't have a clue when it was last charged and I was amazed that it went. Then again, it was a good brand and probably quite expensive.
If starting a car with one of these, connect it directly across the battery and let it rest for a minute or two before charging. Some charge will migrate to the vehicle battery during this time and you won't be up against the relatively high resistance of the battery pack on its' own.
At the consumer end of the market I would wait until they're on special offer at Maplins. Got one for 20 quid a few years back. It will get a car started if the battery is just a little weak and they all have fairly cheap no-name lead acid batteries in them, whether 20 quid or 70 quid. If the battery fails replace with a decent branded one and you will have a much better chance. If anything the cheaper ones won't have cheap and nasty circuitry to detect a reverse connection so it's less resistance in series with the output and less to go wrong.
Ditto the compressors. They are all cheap and nasty, IMHO, having said that mine copes fine with glider tyres (60PSI) and it's very handy being self-contained. A sensible pressure gauge would be nice, though, but no gauge on this type of kit is ever accurate enough anyway so always double check with a proper gauge.