As far as I have been able to ascertain, the majority of english medieval pewter moulds were made of whatever suitable locally available stone there was.

About 95% of the 150+ moulds held in the Herbert museum archives in Coventry are of a highly calcerous mudstone, (White Lias) for which the nearest source to Coventry would be Southam, Long Itchington or Harbury. All within 15 miles of Coventry.

As far as I can tell it's about 2.5 on the Mohs scale of hardness.

I got the chance to pick some of this stone up in April 2018, and unsurprisingly, it works well.
(See below for picture) 

I have found a comparable stone, which I've done a fair amount of work in. Kisii stone. An east african pyrophilite (Aluminium sillicate).

Harder stone allows finer detail, harder wearing moulds, and forces you to work more slowly, reducing the "Whoops, I just carved out too much" factor. 

However, there are any number of different stone types you can work in. I started working in Soapstone, which is soft, quick to work, and generally a good beginners material. African Wonderstone is another pyrophylite, a bit softer than Kisii stone. You can even use plaster of paris. Cast some slabs, and get stuck in. It's advantage is that it is universally available, cheap, and easy to work. It's drawback is that it is overly porous, tends to crack, and is very weak, so you can't get fine detail.

Soapstone can have inclusions, little bits of grit and harder crystals that make for difficult working. As you hit an inclusion in the mould you either have to work around it, or dig it out, often leaving you with a lump on your finished piece. If I have to, I will resort to modern tools, and work on inclusions with a Dremel, but you still need to be careful not to excavate too much, nor to rip the inclusion out, leaving a crater.

It's often a bit of a crap-shoot as to whether a batch of Soapstone is good, or junk.

There are at least a couple of extant moulds in Slate, (Three that I know of in the Netherlands, see Medieval Chic) and I've seen a few Egyptian moulds for Gold & Copper in Basalt, sandstone and limestone. (In the Petrie collection)

There are a pair of mould pieces in York made of Chalk.
see Ottaway and Rogers, Craft, Industry and Everyday Life: Finds from Medieval York, pg 2713 

http://www.yorkarchaeology.co.uk/wp-content/uploads/2015/05/AY17-15-Medieval-Finds-from-York.pdf

having now made a couple of chalk moulds, (of wiltshire chalk) It is terribly quick to work, not very good for fine detail, dusty, prone to degrading if there is the slightest undercut/awkward bit of detail in the mould, but, very good for air escapement, large smooth pieces, (spoons!) and nice and light. so, good for particular applications.
Chalk is also not as good a heatsink as denser stones, so there tends to be more crystalisation in the metal as it cools. (You Don't get the quick flash freeze that you get with a better heatsink.)

Cuttlefish bone is another medieval medium, but only good for a few casts.

Buying stone:
Various artist supply shops will sell soapstone. It can be a bit hit and miss for quality.

eg, https://www.greatart.co.uk/ceramics-moulding-sculpture/working-with-stone/soapstone/ 

In the UK I've found Maltese Limestone for sale, and it works well. It's fairly soft, but quite even, and works quickly. It does tend to be a bit variable in coarseness. Some slabs i've got are just too gritty to work. 
Try https://southern-stone.co.uk/limestone-blocks

Lithographic limestone can be bought. It is worth the money.

Slabs of engineers chalk can do the job, though they tend to be thin, which limits your exploration into 3part moulds
https://www.waltersandwalters.co.uk/engineers-french-chalk/engineers-french-chalk-soapstone-panels-80-60-10-mm 

African soapstone Sculptures in second hand shops are worth looking at to see if there is enough stone in them for a mould.

If you are in North America, you are in Luck.
http://www.giancarlostone.com

Europe:

https://specksteinladen.de/

Australia: Oxlades in Brisbane will ship you Green soapstone. I cant speak to the quality,
https://www.oxlades.com.au/soapstone-green-sold-per-kg

There are a couple of old soapstone quarries that I've been told about; South Australia "old soapstone quarry in the hills on Jackson Hill Rd. Some lumps just sitting on the verge. Quality variable, but plenty there." And reliable reports of similar in Western Australia. 

Where to get your stone from if you can't just buy it?

Wherever you live, there will probably be stone. 
Ask a geologist. Tell them what you need the stone for, and let them tell you what you need and where to get it.

You need a homogenous very fine-grained, or Lithographic (non granular) stone.
Mudstones, limestones, or other sedimentary rocks. (If I were in America, I'd be looking into Minnesota Pipestone.)
Preferably around 2 - 2.5 on the Mohs Scale, harder than that they get Very slow to work, softer is ok, but reduces the level of detail you can get
It should be free from inclusions.
It should be relatively free from Fracture lines. (This can be problematic in Geologically active areas. I'm Looking at you NZ)

Ask, and someone else will tell you where to find. 

Of course, once you have your stone, you'll need to cut it up

Cutting Stone