Brian Stewart :
Will that be enough for Plex?
Plex's requirements only balloon if you're going to have multiple simultaneous connections which require transcoding. It's usually tablets and phones which require transcoding, and if it becomes a problem you can always do a one-time conversion of the video on your PC into a format the phone/tablet can play natively (check the fast decode option in Handbrake). A dual core i3 can definitely handle one transcode (honestly even the newer Pentium and Celerons can do it), probably two simultaneously. If Plex doesn't have to transcode, it's just a glorified file server and even an Atom or ARM CPU could handle it.
For systems which will run 24/7, I highly recommend making it a priority to keep the Wattage low. If I'm doing the currency conversion right, average UK residential energy price is 15 pence/kWh. So a system left on 24/7 (8766 hours in a year) will burn 8.766 kW in a year per Watt of consumption. So each year it'll cost you £1.315 per Watt to keep this running. If you buy a NUC (uses mostly laptop components) or a laptop which burns about 8 Watts, then you're looking at a bit over £10 per year in electricity. If you go with a full desktop build which burns 30 Watts when idle, it'll cost you £40 per year. If you try to re-use an old desktop which burns 100 Watts when idle, it'll cost you £132 per year.
So even though something like a NUC may seem more expensive up-front, it will probably save you money in the long run. If you really want to save on cost, I usually recommend buying a used laptop with an ethernet port and using it as your Plex server. Ones with broken screens can often be found for free or close to it (use an external monitor for the initial setup). Either replace the built-in HDD with a 1-2 TB model, or buy an external HDD and plug it in.