Well T, yes you are correct per the size/quality/length of the cable does matter but there are many other items that need to be considered - but don't be frightened, its all simple stuff.
First decide on the aerial and where you are going to fit it. The simplest answer is a small multi-beam wideband aerial on a pole, and said pole can be stuck into the ground adjacent to your jockey and held vertical by zips or Velcro straps around the jockey shaft You need a wideband (that is frequency wideband) to be able to get all of the used frequencies. You could also push it into the ground and zip to one of the front grab handles. You can either use a multibeam aerial (one of those criss-crossed types) or a log periodic which just has 'prongs' of different lengths. The log periodic usually has a lower wind loading which you have to consider.
You will then need to get some cable and connectors and find a method of getting the cable into the van. More on this later.
Finally it is a good idea to get a small simple variable gain signal amplifier in case the transmitter you will use is a bit distant.
Cable: The old type TV cable, usually brown covered, is (thankfully) no longer available. Today you will get ??100 cable where ?? is two letters such as WF or NX by manufacturer choice. DO NOT buy CT100 if it is offered as the braid and foil inside the cable are usually aluminium and will corrode if they get wet; the other cables are all copper throughout. I would suggest a 25m and a 10m reel, a pack of F-type (also called satellite) plugs and a pack of ordinary (known as Belling-Lee) TV plugs. To get the cable into the van, the fact that you need to wire it suggests it is older so will probably have an external battery box which may also have the mains connector inside. If that is the case then there will be a gap in the door frame of the box to get the mains cable in and there will be room to get the TV cable alongside it. You can get a 'barrel' adapter to connect two cables with F-type plugs on them. Search a bit and you will find a barrel but one that is a bit longer than others and has a nut on it so that you can fit it through a panel. You can then run a length of cable fixed inside the van from the barrel to the TV or aerial amp location. Now when you get to site all you have to do is erect the aerial on its pole and connect the other end of its cable to the fixed connection in the battery box.
The reason for 10m cable and 25m cable is so that if you are on a site that has TV fed from the power pillar you will have a long enough cable (25m) to get from the pillar to the battery box. Note that pillar signal strengths are usually significantly higher than from an aerial so a second barrel so that you can by-pass the amp is a good idea. The 10m cable? Well, you have a wiring job to do and it is always better to have too much cable than too little!
I would recommend Toolstation or Screwfix (in that order) on prices for your bits and pieces.
Per fitting TV/F-type connectors, there is plenty of on-line help in how to fit them. There are also plenty of apps for your mobile phone to show you which way to point your TV aerial.
Finally another thought. Have you considered getting yourself a Freesat box as a signal source? Yes you will need a dish and small tripod on which to mount it but you are pretty well 100% certain to get a TV signal which you may not be with terrestrial TV. If you select this route, download (Android) an app called Satellite Director which will show you exactly where the bird is in the sky (sat signals don't work too well through trees!) Freesat will also work in parts of NW Europe should you go that way.
Good luck.