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The first one I'd get would be the soundtrack from "Natural Born Killers" to get me tuned up for hunting down the culprit that had the VERY bad judgment to steal from me. Up here in the woods of Tennessee, we still do things the old fashioned way. Not much stealing going on with every house equipped with a double barrel shotgun and owners that have a very low opinion of thieves. Generally called 2-legged varmint huntin'. Makes for a much more crime-free environment.
Assuming the insurance payment came through, I'd replace about 75% fairly directly, with the 25% I didn't replace being that which I'll probably never listen to again anyway. I have a complete record of all the CDs I own, so it wouldn't be too time consuming to do.
More to the spirit of the question, while waiting on the insurance check, I'd run out and get copies of my CDs by Tool, Galactic, Al DiMeola, Counting Crows, Gary Moore, John Scofield and Matthew Sweet - some of my favorites across several different styles to tide me over. -Kirk
Since I am mostly an LP guy, I would call Classic Records, Acoustic Sounds and then visit EBAY and Half Price records and begin replacing what was lost.
As to artists, whatever I managed to find first. I would eventually want everything replaced, or at least as much as possible. Some items in my library are nearly irreplaceable.