A B16A2/3 in a 94 civic should be a bolt in swap. A JDM B16A is not and it would be a major pain in the ass, not worth the hassle. For the B16A2/3 swap you'd need to wire up the VTEC and an aftermarket shift linkage kit would be needed, I think Hasport makes one.
As for your transmission, you'll want to find one that was built for the engine. Your current one will waste power, fail quickly, or just not work at all (I'm not sure which one, I just know it won't work). You say you want to keep it automatic, but I suggest that you reconsider. Automatic transmissions don't deliver 100% of the engine power to the wheels, manuals do. I'm guessing that you're looking into this swap to make your car go faster, and it will plus there are more options available to upgrade the engine and get more power out of it, but so much of that power goes to waste in an automatic. You can line up two identical cars for a drag race; one with an automatic and one with a manual, and the manual will win every time. You do also lose fuel economy with an automatic.
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"Ok, systems check; the battery is discharging, the oil temperature is very high, the oil pressure is very low, the engine temperature is off the end of the scale, I'm running out of petrol... but the clock is correct!"
-James May, in an old, worn out Lamborghini purchased for less than £10,000.
