To be honest, it’s not the rod and reel that catch the fish, it’s the bait and the presentation/timing. There is a huge variation in fishing across those areas you mention. Bristol channel has huge tides which would call for big grip leads to pin the bait to the bed, and strong rods to cope. But the solway could easily be spinning for bass at first light.
One thing I’ll say, cheap fishing rods just feel horrible to use. Same for reels.
For a bit of all round I’d suggest a 13-14ft rod (the longer rods help keep your gear off the base of the rocks you’re standing on as you bring in fish or piles of weed), as expensive a fixed spool reel as you can afford (think £75-80), some good high quality mono line and then from there you can read up and tie any kind of rigs you want with a few basics. I’d sooner put cash into a reel than a rod.
Shakespeare Salt are good, though it’s been a few years since I’ve been fishing, I’ve done it all my life to the point of obsession! I have an excellent shore rod I don’t need and would sell but postage might be a pain. It’s a 13ft Greys PZ match Mark 1 and I’d only want £40 for it.
Bear in mind it’s winter and catches will be slow. Fishing will be best when the sea is coming is coming onshore, a steady rolling swell is better than a harsh smashing chop. Use 5-6oz grip leads and either peeler crab or bluey for bait and pin that bait to the bottom and don’t move it. The bigger evening fish will home in on the smell.