you have many options..
*get a sir I w/ auto tranny
good - auto b16a tranny probably has better ratio than you ls..
bad - the b16a1 auto motor has less power than b16a1 manual, the loss in power is in the cams...the cams suck...the valvesprings and retainers are different also which will not allow you to rev as high as a manual...
*get a sir I (manual) longblock use ls auto tranny
good - will save yourself the most money
bad - less power than a jdm b16 sirII
*get a b16 sir II longblock
good - most power from the options that you want...170hp instead of 160hp due to 10.4 compression instead of 10.2
bad - more expensive than b16a1 longblock...almost twice as much

I'm not sure if the b16 sirII has an automatic option...i'm assuming it doesn't...anyways if it did...you MAY need to get a custom bracket to make that transmission fit...

my opinion: get a b16a1 longblock...since you want to keep it automatic i see that you really aren't trying to go that fast...changing the transmission over is just as important as changing the motor...the automatic transmission will hold you back...