I know that this is familiar information for most of us, but I think the first thing we should do is go over the steps for casting a spell. Especially since they have changed with the 4th edition printing. According to the rules on page 13 of the 4th edition English Rules, the steps for casting a spell are thus:
Step 1: Declare Spell
This is the step where you select your target AND choose the exact effect that the spell will have if there are multiple possible effects. For example, with [mwcard=MW1I07]Dissolve[/mwcard] you would choose both the Mage you are targeting, and the specific equipment that you wish to destroy as an effect of the spell.
Step 2: Pay Costs
This is the step where you actually pay for the spell. The cost of the spell may be affected by your choices in Step 1, such as with [mwcard=MW1I07]Dissolve[/mwcard] where the cost is equal to the casting cost of the equipment you selected for destruction.
Step 3: Counter Spell
Nothing happens during this step unless it specifically says it can.
Step 4: Resolve Spell
This final step is where the spell actually takes effect and does as you've intended. If it gets to this step, it is too late to stop it from happening.
It is also important to remember that a spell's text box isn't just used to describe it's effect, but is also used to clarify how to handle the spell during it's casting. Such as [mwcard=MWBG1I02]V'Tarrian Healing Song[/mwcard] restricting the target further than just a Living Creature, to one within the same zone as an orb you control. That's not an effect of the spell, it is clarification on targeting during the casting of the spell.
Now, let's finally take a look at [mwcard=MW1I20]Purify[/mwcard]. I 100% agree that this spell could be better written and is somewhat confusing to look at. First thing's first, the casting cost is listed as X, which we know indicates a variable casting cost which must be paid during the Pay Costs step. When a spell has a variable casting cost, it will tell you how to calculate that cost in it's text box. I really wish that Purify followed the same pattern as Dissolve with a line that read "X=this casting cost", but it does not.
Instead, the text box of Purify makes it sound like you neither have to select what you're removing nor pay for them until the Resolve Spell step. Especially since you don't handle the Enchantments until after the Conditions have already been removed completely. The magic rule which says that specific card text overrides general rules would allow it to do this as well. However, we still have to pay for the casting cost of X before we can even get to the Resolve Spell step, and we don't know how to calculate that cost. That does not mean it costs 0. Saying that we know it is 0 because we don't know how to calculate it makes no more sense than saying it is 2 because we don't know how to calculate it. We simply don't know and would have to leave it at that.
So, either the text box is poorly written and the spell is supposed to be handled the exact same way as other similar spells, such as Dissolve. Or, the variable casting cost of X is a typo and we don't know how much it actually costs. I am inclined to believe it is the former, and that is how I would personally play it. The other option would actually make it unplayable currently.