The general rule is have these with you in the car
1. Windproof/Waterproof top
2. Windproof/Waterproof trousers
3. Waist bag
Also it is a good plan for longer events to have a hat and gloves available.
So then the agonised question is - "Do I have to run with all of this?"
Only if the race director says so or more usually you make a decision on how you think weather looks and take what you think you will need. I would estimate that of the fell races I have done which must be over 100 that kit has been enforced (or has been an entry requirement) maybe 20% of the time.
Apart from this I have carried an extra top probably 10% of the time.
"I have never used a compass- what do I do?" - Well I have never needed to consult one in a race as I haven't done the more orienteering end of things but if you are a total novice with no mountain experience then you probably need to get some before taking on a race that is not marked or is of any significant distance. Actually beyond running it is a useful practical life skill to be able to work out where you are which is to my mind 80% of navigation.
The idea of series such as the South Wales Winter Series is to get people used to mountain races in a relatively safe manner where navigation is not really an issue, but it can never hurt to have an idea of your surroundings.
Shoes - there is nothing stopping anyone doing a fell race in road shoes other than common sense and there is a whole spectrum of off-road shoes from slightly tarted-up road shoes, trail shoes, cross-country shoes (not spikes) to fully studded fell shoes. Inov8 have a shoe for every conceivable terrain.
The definitive retailer is www.peteblandsports.co.uk/
The definitive Inov8 model for fell racing is called Mudclaw