A third party processor would be something like Paypal I assume?
Would this method be the shortest short term solution?
Well, yes, and no. Paypal is more of an e-wallet system. A Third Party processor, (also known as an IPSP), utilizes a mastermerchant account, that you would have a sub account with. They provide all of the features that you need to run your site, but are more expensive that direct merchant accounts.
Examples of that include ccbill EU, verotel, etc...
If you would like, you can contact me for more advice regarding your particular business model. Paypal has certain restrictions, as do third party processors, and there are some people that are adverse to dealing with a merchant that only uses paypal....
I would be happy to help you out with this, and try to steer you in the right direction.
All in all though, if you are just starting out, going with a third party processor of some type is probably your best bet.