Agreed you could do it with a hole saw (without centre pilot hole if you need a plain disc - no centre hole). As said, a jig + pillar drill would be a must if no centre hole is required.
What would also work is any powered fret saw/scroll saw, if you can beg/borrow/steal the use of one. It would need a bit of practice to get nice clean circles, AND a reasonably fine-tooth blade, especially at 3 mm thick, but there's a huge range of blades from people like Pegas (Axi are the UK stockists) and this is definitely do-able this way.
Re material, I agree that this thickness is probably classed as "plate", not sheet, and also agree that flat bar of the appropriate width will do. As to where to buy, I guess that it's going to be expensive if buying new (do you have any local steel stock holders?), or purely by luck, a bit of skip diving, and/or talking to local metal working companies about their scrap bin. This last is probably not too helpful though, because if want decent quantities they'll be selling their scrap to the local scrappy (have you heard about gangs stripping cables from road and rail sides for the copper value)? Copper is a pretty high value metal these days.
IF it is OK from the looks/strength viewpoint (you don't say what the job is) you could try cutting these from thinner sheet and then sweating them together (solder) to get the thickness you need. At 3 mm thick with say, 0.8 mm sheet as a starter, you'd need a hefty solder iron though - preferably a pair of old-fashioned heat up over the gas jobbies because copper is a great heat sink and those old irons hold a lot of heat.
I inherited a set of number/letter stamps from my Dad in the '70s, not sure what make. For new I suggest you look at the suppliers sticky at the top of this General Metal Working section - people like Arc Eurotrade spring to mind (usual disclaimers).
HTH
Edit for a P.S. If you go through the sticky at the top of this section "Hacksaws, blah, blah, ......... " you'll find info on a quite cheap (50 quid or so???) little electric drill attachment called a nibbler. Again with a bit of practice, that will cut nice circles (without a centre hole) in any sheet metal up to about 2 mm thick, but that tool will not handle 3 mm material. And of course, the other possibility (for centre-less discs) is a powered jigsaw, again fitted with a suitable fine tooth metal cutting blade.
If you do go the thinner discs stuck together route, you can mount the stacked discs (after soldering or whatever) on a mount made of a ply disc with a metal shaft screwed into it, all hot glued onto the back of the stack. That can then be mounted in a pillar drill (or electric drill in a horizontal stand) and spun against a file (gently!) to true up the resulting disc.
That was my "after my shower afterthought"!
