Sorry to hear about your hens but you seem to have acted quickly but be extra vigillent over the next few days as once the fox knows there's easy pickings they'll be back. Your new fence should do the trick though. We’ve used nets for 10 years now without losing a chicken though when we used to let them wander over our side meadow we had problems. If you want to bait the net, and it's probably not a bad idea, use bacon rashers wrapped round the fence so the fox needs to get its tongue round it and then it’ll be sure to get a belt. They won't go near it after that.
On the choice of battery or mains powered if you have a convenient mains supply handy and you don't want to move the net at regular intervals, over fields, then mains units are a good choice as they are always on and don't obviously run down like batteries. However there are safety considerations with mains units which you MUST pay attention to and I can't comprehensively cover in a post. There are strict rules about using mains outside and you should use a qualified electrician who can do certified wiring if you need to do this.
If you use a mains unit then you can (and arguably should from a safety perspective run the high tension (shock) conductor from your energiser (which should be located in a building for weather protection) to your fence directly. This will require a special weather-proof high tension voltage cable which will be quite expensive so what you save on a battery you might spend on a high voltage cable.
If you live in an area where you have mains outages (as we do in the country) or need to have a movable net, or there's no convenient mains supply, or your worried about a potential safety issue (children or walkers), or you just don't want the expense of the services of an electrician, then batteries are a good choice. I use a 12V wet LEISURE battery not the dry 9V type which can't be recharged though has the advantage of being light and easily portable for field use. Rutland market very good quality energisers for both mains & battery, though they aren't cheap.
You can have the best of both worlds and solve the safety issue by using a wet battery inside a shed (or stable in our case) with a car battery charger on float, keeping it charged. Then run a twin conductor 12V power cable to your energiser situated on the fence (no shock safety issues with this but make sure it can't short out and use an inline 2Amp fuse at the battery end to protect against a fire risk). Do this rather than run an external mains cord which has safety issues and is not what I'd recommend. If you use a battery on charge then your fence will stay live even with a power cut or your circuit breaker trips or the cleaner unplugs it.
A note on wet batteries - obviously an old 12V car battery can be used and is cheap but it won't last long unless you keep it charged. If you completely discharge a car battery repeatedly, the plates warp and short out the interior cells making them useless. Leisure batteries are designed for repeated deep discharges and have specially reinforced cells which take this treatment so if you are buying a battery make sure it's a LEISURE battery designed for frequent deep discharge cycles. Check out ebay for cheap ex computer/ telecoms uninterruptable power supply batteries which are usually very high spec. batteries and get routinely replaced after so many years (light) service. They normally have lots of life left in them but you obviously take pot luck.
If you use an electric fence in open fields expect to have to have it repaired ocassionally as lightning strikes on the fence or nearby can easily zap your energiser. Cheaper units are usually more vulnerable than more expensive well designed ones.
Regards