The 2011 has a weak CPU itself, so I suppose your internet uplink bandwidth is less than 50 Mbyte/s and you plan no heavy traffic among devices in the home network (such as video streaming from NAS to wireless devices).
If the above assumptions are correct, then even hAP mini will do, but it has only 2.4 GHz radio and doesn’t have PoE-in which is one of your requirements. I’ve circumvented this by using a passive PoE injector set and a universal passenger/truck USB charger to convert the 24 V DC provided on the passive PoE output to the 5 V DC required by the hAP mini (some soldering is required). cAP lite is $10 more expensive but has passive PoE in, so no fiddling is necessary.
If you want more wireless bandwidth, or need the 5 GHz band, or don’t want to fiddle with voltage converters, the next choice is hAP ac lite, which still has got only FastEthernet (100 Mbit/s) ports but one of them is PoE-in.
If that’s still not enough, the best value for money is still the hAP ac², which has a much better CPU than the 2011 so it makes sense to use the 2011 only as a switch and do all the CPU-intensive tasks on the hAP ac². However, there’s a minor PoE issue again, as the 2011’s PoE-out port is a 100 Mbit/s one, so you’d have to use the passive Gigabit PoE injector set and a short patch cable to extract the DC voltage from ether10 (PoE out at 100 Mbit/s) and inject it into the cable running from one of the gigabit ports (ether1..ether5) towards the hAP ac² (no soldering required).