Was there a barter system in place, or did goods hold an established value that moved with the ebs and tides of the local economy?

It's difficult to say for certain what the different costs of items were and how exactly the local economies varied. Barter would certainly have been part of economic transactions in areas with a shortage of hard currency, but the currency economy was very much one of the defining features of Roman power, and Roman currency has been found even far outside the bounds of the Empire, indicating that it's use extended pretty wide.

How were coins measured/denominated out against one another? We're silver and gold king as far as purchasing power went? Or we're other base metals used to extend the currency supply?

There were three basic types of coins that were used. At the top, you have the gold coins like the Aureus and the Solidus. These coins were not used in day to day transactions, and were for the most part coins of account, or for large transactions. In general, possession of these coins would be limited to the wealthier classes, and they remained relatively pure throughout the existence of the empire. Next, you have the silver coins, the most famous of which was the denarius. This was the coin that was probably the most important, and was roughly equivalent to one day's pay for a soldier or labourer. This coin suffered from serious debasement throughout the Imperial period, falling from roughly 90% silver in the early days of the empire to less than 10% by the end of the third century. The debasement of this currency was primarily because it was the way soldiers would be paid, and as the largest outlay of the Imperial treasury, when you needed to pay your soldiers as an Emperor but didn't have enough money, the easiest way was to debase the silver content of the coins. Various attempts were made to reverse the debasement, but it's of course a lot harder to build confidence in a coin's value than to lose it. Diocletian introduced the argentus as a substitute, doing away with the denarius completely (although it continued to circulate). Finally, we have the various copper and brass coins that would be used as day to day coins to buy your food etc such as the sesterce and as. Because of the debasement of the denarius, these coins also lost much of their value, since theoretically their value was pegged to their relationship to the silver coins. If I was going to try to put this in lay terms, the best way to think about it would be silver would be your bills and the bronze and copper coinage your two dollar and dollar coins, although bronze and copper coins had significant more buying power. Gold on the other hand was not a coin you would be throwing around willy nilly. If you had a solidus, that would be equivalent to having a $100 bill or more. How often do you buy a can of soda with $100 bill?

Did a credit system exist between merchants or patrician families?

Rome has a long history with credit and banking. Money lenders were part of the fabric of society, and many of the social conflicts going back to the early Republic dealt with debt relief. In terms of large transactions, much of the wealth was not in hard currency but rather merely lines in an accounting notebook; if you sold property worth 100,000 sestertii you weren't expecting a wagon of bronze or gold coins, but rather something like a cheque as a form of payment. The bankers (called argentarii) kept track of the money and theoretically could offer payment on request. If you traveled from one part of the empire to the next, agents of those bankers would be able to provide you hard currency from your accounts as needed, or you would carry a promissory note from one argentarii to another; basically, a bank draft. Indeed, much of the business of the Empire was conducted on paper with physical money never changing hands.

Was there a established standard system of weights, distances, etc? Or did this vary from region to region across the empire/peninsula?

This is a little more difficult to answer because really the answer is: it depends. While Rome itself had a relatively exact system of measures for both weight and distance, other parts of the Empire had their own measurements that had very long histories. While local measures would have survived, within institutions of the Roman empire, the Roman equivalent would have been paramount. The most important institution was of course the Roman legion, and wherever these men were stationed they would almost certainly use the Roman measurements for their constructions and work. The use of local units was mostly going to be determined by the development of those units in pre-Roman times. So, for example, while the West mostly would have adopted roman units, the East, which already had several entrenched units locally, from Greece to Egypt, would likely have been slower adopters.