If you do take the dip, I'd suggest waiting until at least 6th level. You'll want to be able to disarm magical traps by that level. However, you'll probably want precise shot before 7th level, making the dip less effective. Honestly, I'd pass on the dip for you, unless you can stand the pain of waiting to pick up precise shot.
For your spells, be sure to pick up heroism ASAP. It's great for a "set it and forget it" buff that you can throw up at the beginning of the dungeon and will last until you leave. Also, try to find room to pick up arcane strike. You can only use it every 2/3 rounds, dye to needing to use swift actions for putting up your luck, but it is still a good damage boost.
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Deadly Aim is better than Arcane Strike. Which means you should get it first, not that you shouldn't get both. And Rapid Shot is better than either, as is Manyshot. Still, those should probably be your next four Feats (okay, Clustered Shots maybe before Arcane Strike).
Actually, thinking about it...if what you mostly want is Precise Shot, you can get it as a 4th level Archaeologist by burning your Rogue Talent on Combat Trick. So I'd do that. Grab Rapid shot at 5th, Deadly Aim at 7th, and Manyshot at 9th.
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You're missing Precise Shot, and would strongly benefit from Deadly Aim and Rapid Shot as well. I'd suggest a 2 level dip into Fighter, likely with the Lore Warden archetype to let you maintain your skills as much as possible
He can get two of the three in the next two levels sticking with Archaeologist. As I note above.
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The thing is, for practical purposes with Archaeologist's Luck and buff spells...you're better than many full BAB classes in to-hit.
At 7th, assuming equal stats, +5 to hit from BAB +3 from Archaeologist's Luck is equal to a Fighter's +7 BAB and +1 Weapon Training. And that's without Buff Spells, which can easily add another +3 or more.