Mystic Fire Knight would replace Levels 1,2 & 4, so IMHO SotAO could be taken with the first Level in Prestige Paladin.
Unless you're using a different version of SotAO from me, you can't take that with the first level of prestige paladin. You've got the first problem of: Prestige Paladin != Paladin, requiring a DM intervention. The second problem is: SotAO requires you to have 4 levels of ranger or paladin, so even if you were allowed the prestige version, it'd be PP4- which is another 2 levels of spells lost. It's even worded in SotAO that you use your *paladin or ranger* spell slots to prepare the arcane spells, of which you have none (again requiring DM intervention to turn your prestige paladin's archivist slots into ersatz paladin slots).
The final problem is: why are you doing this? The beauty of the Archivist is that nearly every single useful sor/wiz spell can be found on an obscure domain list somewhere. You can just roll up Archivist 20 and go to town; if there's one or two spells you absolutely *must* have, check out the Hexer PrC. It's unreconstructed 3.0 material, but since it was never replaced it's just about as "technically valid" as your dodgy use of the prestige paladin. Plus, Hexers kick butt- full BAB, gaze attack, 5 sor/wiz spells added to your list (creating all sorts of confusing results- could you learn a divine-ified sor/wiz spell from an NPC hexer?) There's also Divine Bards who can provide you with the entire Bard spell list.
The final trick is that it is also theoretically possible to create a divine-sourced scroll of any arcane spell, using an Artificer (or, IIRC, a Warlock) to create it. Such a scroll would only be a curiosity in a normal game- the only way to use it is via UMD. But to an archivist, it could maybe count as a divine scroll that you could learn from.
But even without those funky tricks, you can get plenty of spells to cast on your own. Check out the domain list in the PHB and SpC for all sorts of goodies- haste is in the time domain, teleport, grease, even Evard's Tentacles. Heck, you can get Identify as a lev1 spell (oracle domain), and when cast by a divine caster, it has no 100 gp pearl cost.
As an aside, I just created a new Archivist for a game (my Totemist died ignobly), and will probably follow up to this thread with an analysis of useful spells in the next few days.