Is there anywhere that they explicitly say the minimum, like with maneuvers?
Yes, it's based on the Spell in question which is not a tautology as Link mistakenly thinks it is.
Unlike Maneuvers, a Spell's Level is highly variable. So if the Spell in question were say a Wizard's Animate Dead. The Wizardy powers needed are seven because to a Wizard only having a caster level of six is not high enough to cast 4th level Spells. But if there Spell in question were a Cleric's Animate Dead you only need a caster level of five because to a Cleric it's a 3rd level Spell which only requires a caster level of five. And there is no mix-and-match unless you use a Known expanding trick, Animate Dead does not require a Cleric to have a caster level of seven because it appears on the Wizard List any more than a Wizard can claim he only needs a caster level of five because it appears on the Cleric List.
So the minimal CL of a Spell is, as the entry states in plain text, based on the Spell in question. There is no stated requirement of forced Spell List association order for creation so it's possible through alternative Lists to produce lower-than-average items, such as a CL1 Wand of Haste by having a Trap Smith cast your Spell. But for the discussion at hand, Magical Item DCs, it's best to handle the deconstruction using SLA's order of assumption. And that is calculate the Spell DC as if a Wizard had craft it, or if his default list is unable to assume a Cleric did, then Druid and so on.
and now im curious about things that penalize your caster level. like +x to one thing and -x to all others.
seems like that could get weird.
Try Energy Drain some time, for the purposes of die rolls and calculations you have a -1 penalty to your effective level. Some people treat your CL to be a formula, meaning if you were 18th level and hit by two negs you can no longer produce 9th level Spells.
But the FAQ says that's wrong. In one entry it confirms you don't automatically lose access to a Spell Level via Negative Levels and while it doesn't explain why, it's entry on Bloodlines confirms what the encoded thought (aka the word 'calculation') actually means. Energy Drain has an effect on Caster Level Checks since they are roll, but not on checksums. Like if you wanted to ignore the FAQ and claim otherwise well you can just as easily claim HD is also such a calculation. You "calculate" HD by adding up the number of Class Levels and application of various Abilities such as Inspire Heroics, so a 10 HD creature with five Negative Levels totally has 5 HD right? Well that'd mean he has as many Negative Levels as he has Hit Dice, he died!
So if you ruled otherwise, that CL is a "calculation", the same concept when carried through would affect all kinds of various things unless you started tacking on dozens of additional exception rulings to it. Which as I'm sure you can guess, can lead to a massive debate full of screaming on both sides on how to handle everything.