My question is, should I (or do you) always play with Platinum and Colony even when you're not using Prosperity kingdom cards? Or do you only play with them if you're doing a Prosperity only game? Or do you use them whenever some (or certain) Prosperity cards are chosen as kingdom cards but otherwise you leave the Platinum and Colony to the side?
From the Prosperity rulebook:
If only Kingdom cards from Prosperity are being used this game, then the Platinum and Colony piles are added to the Basic cards in the Supply for the game. If a mix of Kingdom cards from Prosperity and other sets are being used, then the inclusion of Platinum and Colony in the Supply should be determined randomly, based on the proportion of Prosperity and non-Prosperity cards in use. For example, choose a random Kingdom card being used - such as the first card dealt out from the Randomizer deck - and if it is from Prosperity, add Platinum and Colony to the Supply. Platinum and Colony are not Kingdom cards; when those are included, there are 10 Kingdom cards, plus Copper, Silver, Gold, Platinum, Estate, Duchy, Province, Colony, and Curse, in the Supply. Use 8 Colonies for a 2-player game, or 12 Colonies for a game with 3 or more players.
Seems like there isn't much I can add to that!
Yes, there is what the rulebook says for choosing randomly.
But there are two primary effects of these cards and honestly I think the bigger issue is which effect matters more for you.
Platinum and Colony extend the depth of strategy you can put into a build up. They tend to make for longer games, but games in which you could take things further. This is a popular enough option that Androminion on Android has always including these as one of its settings. Personally, I really like this effect and we usually include them in any setup.
On the other hand there are various cards in Dominion that seem to have been written on the tacit assumption that Gold is your final treasure goal. Sure, they can be used regardless, but they are just less likely to be bought when platinum is in play. If that is something you want to avoid, then leave them out. (Other cards, like Mine, become more powerful, but not overwhelmingly so).
The Second Edition of Prosperity actually made an update to the rules regarding Platinum and Colony usage. What was previously declared as "the rule" is now just a suggestion on how to randomize if you wish. The official "rule" now is that you can include them whenever you want to.
Prosperity includes two new base cards, Platinum and Colony. You can include them whenever you want to; they are always used together. If you want to determine when to use them randomly, choose a random Kingdom card being used, and if it is from Prosperity, use Platinum and Colony.