The difference between a jump starter and a deep cycle battery? Minimal.
The starters have a deep cycle battery in them, most use a 7Ah SLA(Sealed Lead Acid) or AGM(Absorbtive Glass Mat) battery, some more expensive ones use a 12Ah or 18Ah one.
As Brendan said, you're better off in the long run buying a decent SLA/AGM battery and a proper multistage charger for it.
The bigger the battery you buy, the longer it will last.
This is due to DOD, or Depth Of Discharge... the less you discharge it, the less it has to work.
Regularly taking a SLA past 50% DOD(12v measured under load) will shorten its life considerably.
Also, Lead Acid batteries like to be maintained at full charge... so get a decent(computer) charger and leave it connected whenever the battery is being stored, 'floating' the battery.
If it is stored for extended periods partially charged, the battery will 'sulphate', at which point you may as well get rid of it.
Basically, Lead Acid batteries like to sit around and do nothing but eat(electrons from the charger) their whole life.
If you would like to learn more about Lead Acid batteries, there is a very good write-up here:
http://www.windsun.com/Batteries/Battery_FAQ.htm