Bear in mind that we have much higher welfare standards for farm animals in the UK, especially pigs. I would never buy pork that wasn't from pigs that were reared in the UK for that reason. This is reflected in the price. If it is very cheap then it will have been imported from a country that doesn't look after their animals very well.
If you've got a slow-cooker look for the cuts that are ideal for casseroles, pot-roasts & braised dishes. They tend to be the cheapest and most flavoursome.
Beef skirt or shin beef are delicious. Brisket makes a terrific pot-roast and isn't expensive at all. Shoulder of pork and shoulder of lamb both work great in casseroles or pot-roasts and they tend to be at the cheaper end. Chicken thighs tend to be better in slow-cook dishes than chicken breast and same applies.
What to look for.... good colour (not pale or dull) & plenty of 'marbling' or thin streaks of fat running through the meat which make it juicy. If you can get 'matured' or 'grass fed' that's going to be more expensive but taste good. You can go organic which is more expensive again. All depends on your budget.