I buy a Sainsbury's own small gammon joint (unsmoked) as it's a reasonable price and I like plenty of meat in my soup so it makes a hearty meal. If you have a local butcher or your supermarket has a meat counter you could always ask if they have some ham off cuts and a ham bone, this would work well as the bone would give a lovely flavour.
I cook mine in my instant pot (electric pressure cooker). I soften onion and celery in olive oil or butter, usually add a couple of carrots, then I add (washed) dried green split peas, low salt veggie or chicken cube and black pepper, but no salt - this can be added at the end if needed, but it often isn't as gammon is already quite salty. Lots of recipes say add bay leaves, but I rarely have any so I might add some dried thyme, but it's down to personal preference. I cook on high pressure for 20 minutes, let it cool, then blitz it with an immersion blender, or in my liquidiser.
You don't need a pressure cooker, you can cook on the stove top, obviously it will just take longer, usually 60-90 minutes. I have also seen recipes online that cook pea and ham soup in a slow cooker. Just try whatever works for you.
Pea and ham soup is my favourite, good luck Op.