Hi John,
Beach and fishing from the rocks or pier is great fun.
To answer your questions. You can fish from the beach at anytime of year but you will catch and need to target different species at different times of year. Spring tides are generally speaking better than neap tides (full or new moon) as they tides are higher. Spring can be a bit quiet but there are still fish to be caught. Winter is good for cod, whiting, flounder and dabs from the estuary. Fishing for cod after a heavy storm is a good time to go as the food will be washed up and floating around mid water and stimulates the fishes appetites. In the summer Bass, mackeral,garfish, pouting, strap conger eel, are on the menu amongst others. Dogfish are feeding all year round and are tasty to eat although they look a bit off-putting. They're sold as Rock-salmon in most fishmongers and restaurants and are easy to catch as they'll eat pretty much anything. A carp rod would be strong enough for lure fishing for smallish bass or a bit of medium weight fishing but you'll probably need a proper beachcasting rod for rocky areas and when there's a lot of kelp about after a storm or rough weather, or if there are conger or big doggies about for eaxmple. A 12ft beachcaster casting 6 - 8 ozs will be perfect, (make sure it's the correct type for the reel you'll be using with it, which will be either a fixed spool or multiplier, and you should be able to pick one up for around £40 - £50 for a reasonable rod. ( abit less even for around £30 for a cheap one but you can get them up to £300 - £400. It's the same as anything in life - you get what you pay for. You should be able to pick a reasonable beach casting fixed spool reel for around £30 - £40 too. Again you get what you pay for but a £40 reel will be perfect for starting out. Muliplier reels are also used for beachcasting but I'd avoid them at first if I were you as they take a bit of getting used to. You need to control the rotation of the drum when casting and slow it down as the lead hits the water. If you don't the water slows the weight down and the drum carries on revolving at the same pace as the cast and you'll end up with a bird's nest (tangle) which can literally take a few hours to sort out if it's a bad one and believe me it's no fun trying to sort out a heavy bird's nest, when you want to get on with your fishing.
20lb main line on your reel will suffice for general beachcasting, and you will need a shock-leader length of line between the weight and the main fishing line on your reel, around 20ft of shock-leader line will be enough If you don't have a shock-leader you will be getting crack-offs nearly every cast and it's dangerous to others around you if the weight snaps off and whacks someone.
A general rule of thumb is 10lbs per ounce you are casting, so if you're casting a 6oz weight, you'll need a 20ft length of shockleader at 60lbs breaking strain 8oz = 80lbs ( 8oz is heavy and usually 6oz will suffice) sockleader etc. Use a half hitch plus a grinner knot to tie the shock leader to your mainline.
Baits - there are loads. Peeler crab is good for bass and mussels are a good substitute as they give off a similar scent' Live prawns if you can gather some are also good. Squid, mackerel strip, rag and lug worm, razor clams, sand eels live or frozen are are all good baits. It really depends on what you trying to catch. Squid strip on float fished light tackle from the rocks is enormous fun for mackerel and the same but mackerel strip for garfish in the summer. Wrasse will take lug and rag worm and are great sport, but strike quickly as they'll wedge themselves between some rocks very quickly. They're great fighters though.
You can keep anything you catch but please observe size limits. As for eating, most sea fish are good but maybe not so good are wrasse, pouting and weaver spring to mind but are all edible. Personally I've never tried these fish but they do eat them in France.
I could write more about specific rigs, baits and tactics for different fish and if you have any specific questions ask away. Good luck and tight lines
BTW - float fishing is great fun in the sea on light tackle. I use a Mustad salt water sport with an Abu cardinal 304R fixed spool reel. A bit pricey though at around around £115 for the reel and rod but will cope with lure fishing, float fishing and light beachcasting in clear water.
There are 3 or 4 magazines on the market such as Sea angler or Sea fishing, crammed with advice and adverts for tackle dealers. A lot of the dealers do Combo prices and you can pick up a good deal on a rod and reel combo.
