The N52 range of engines are fairly bullet-proof and do offer good overall performance/economy for what they are in my opinion. Okay, I am most familiar with the 330i, and not so much with the 323i and 325i, but the basic engine design is the same, so in terms of reliability they all typically have the same strong and weak points. With regards to fuel consumption (spanning a good few years), click on my Fuelly signature - worst fuel consumption from mostly town driving for me has been 12.5 l/100 km which is not bad. Admittedly, I do try most of the time to conserve my fuel, but sitting at a few robots is in many cases all that is needed to spoil all your effort. These things are at their best on the open road, granted, that's a typical ideal situation for these NA 6's.
Things to look out for:
As mentioned, some earlier N52 engines developed a noisy HVA lifter problem (I firmly believe mostly due to frequent short trips with the engine still being fairly cold). There is a so called "bleed" procedure, but it is not at all a fix. A proper fix is either a rebuild of the existing head with new lifters or a new updated head which they released later on, but these apparently also suffered from this. Touch wood, mine has never been noisy and I can only hope that this is thanks to me being fussy about not allowing ANY short trips and the engine is most definitely not driven like a granny is driving it.
Oil consumption varies on these engines - some people see absolutely no oil consumption between services, but most tend to have to top up at least once before the service indicator comes on. So when test driving, check the oil level via the electronic dipstick (no physical dipstick BTW).
Vanos problems are usually caused by the solenoids being slightly dirty and sludged up. This can often be remedied by removing both solenoids and cleaning, then swapping their locations when returning into the engine (they are the same and this is a very common practice). Oil pressure is also quite critical for the Vanos to work properly, so fresh oil and oil filter is something these engines love!
Electric water pump (does not have a normal belt driven water pump) and thermostat are common parts that fail or become faulty over time, and they are fairly costly to replace. No temperature gauge, just a warning light if the engine overheats, but you can check the engine coolant temperature through the hidden menu on the OBC. You can also test the water pump by performing a coolant purge which bleeds the cooling system to remove any trapped air - you will be able to hear the pump going through the motions.
Valvetronic throttle system is also a known area of concern. The Eccentric shaft sensor which measures the amount of valve lift can become faulty often caused by a failed oil gasket on the valve cover where this sensor's electrical connector is located - so typically when the connector is removed, the pins on the sensor are swimming in oil. The actual Valvetronic motor can also fail, but not as much in general. Both parts are fairly costly, the VVT motor is fairly easy to replace, but the sensor requires the valve cover to come off.
DISA actuators (some engines have 1, 2 or none) can become faulty and as far as I know, you cannot "repair" them as you can on the older units found in the M54 engines for example, but overall these are somewhat less prone to fail.
Then the usual various sensors, cam position sensors, MAF sensor, oil level/condition sensor, etc.
Personally, I would suggest the 320d, or a 330d for that matter, especially since you want to go for an automatic. Performance and economy for daily driving is going to be the best overall, and the engines are pretty well made. There are obviously things to look out for there too, and failed parts, turbo etc, can hurt the pocket, especially if there is further damage from the turbo failing.