A good 1k is a good place to start. It also occurs to me that 3k to 10k is a big jump. I might suggest looking into a naniwa 5k or king 6k (Maybe a King 1k/6k combination hone?) To help bridge the gap.

I'm also curious ad to which 3k/10k hone you've got. Not all hones have proven suitable to our purposes here, and honing these is tricky enough with known good hones.