I know people like nice kit. But it depends on how much casting you are going to do.
If just starting out and want to see if casting is for you, then get some cheap/used kit.
A melting pot. That could just be a cast iron pan on a gas burner and a lead dipper. Or a small electric casting pot. Yes the Lee ones are cheap and cheerful, but I've cast many thousands of bullets with them.
As suggested, cast outside, or somewhere with a fume hood/extractor. (Not on your kitchen stove!) You don't want to breath lead fumes..
Protective kit. I just put on a thick crappy old jacket, that covers the arms, a face shield (if you can get one at the mo!) and riggers gloves for a quid.
Moulds, I tend to use the Lee ones here too. Nothing special but they work.
And if you are only doing small qualtities, then the Lee resizing dies are fine. These fit into your reloading press and you push the bullets up with a punch. I use the RCBS lube-sizers, which are nice. But the Lee dies to be honest do the job on smaller batches.
The othet thing no-one else seems to have mentioned is your source of metal.
You can't use pure lead in anything other than muzzle loaders or SG slug. You need some % of antimony and tin.
The quickest way is to buy ingots of bullet metal.
Tin is easy to get and add to your mix. But antimony is a bit of a problem. Wheel weights and printing type used to be good sources of high antimony alloy. But they are not really availabe these days. Trying to make your own alloys is difficult and dangerous (the oxides of antimony are as bad as arsenic.)
So probably safest is to buy ingots of high % antimony alloy here too.
If you have a local range, you may be able to get hold of rage scrap. Which is what I do. Depending what they shoot there, gives you an idea of what sort of range scrap you will get. If they shoot mostly 38 etc, then the scrap may be pretty much perfect casting metal..
You may want to prepare batches of lead ingots and process scrap. So a good size cast iron pot and gas burner is good here.
Care is required though, lead explosions can be quite unpleasent. Though the results can be quite pretty, if you get away uninjured. Peeling a huge, 1/8th inch thick lead doiley, off your workbench (and fence, and neighbours wall,) can take some explaining.
But once it is in little 8oz ingots, it's a bit safer to work with.