I’d like to mount a small stone disk - 5mm diameter, 2mm thick - into a rather large acrylic block, with the top of the disk flush with the face of the block. Reading up on this, it seems that brad point bits are a possibility, maybe mounted in a router with a precise depth adjustment, would be one approach, but this will leave a small dimple in the bottom center of the hole that I’d prefer to avoid. Somewhat stumped here, and I don’t want to spoil a 2" thick hunk of acrylic (although I can certainly practice on thinner pieces) but also don’t want to buy a whole lot of equipment to create what will probably be two, maybe three holes.
What tools do you have to work with?
I have found these bits to work with acrylic:
- End mills
- Step bits
- Forster bits
- Brad-point bits
- Standard bits sharpened at steeper angle
If you need a flat bottom I would try the end mill.
Run at slow speed, go slow and use a lubricant
Don’t let the bit build up plastic. Pecking may help.
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I have a fairly decent drill press. I’m not averse to buying a router, I’ve been meaning to do so for a while now.
I would start with an end mill in your drill press.
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I agree with @donkjr on this one! For buying a router, what kind did you have in mind?
With a handheld router, you could create a much larger circular template and move the handheld router around inside that circular template to produce a smaller circular cutout.
With a CNC router, of course you program it.
Which kind did you have in mind?
Edit: never mind, I read mm as cm the first time through.
A plunge-cutting 5mm endmill (which won’t have a hole in the middle for through coolant) in your drill press, as @donkjr suggests, makes good sense.
Do you have a depth stop on your drill press?
To reduce chip packing that could mar the acrylic, I’d consider a 2-flute square endmill instead.
My drill press has a depth stop, but it’s very crude; it would probably take me a solid day to get it dialed in to anything precise.
No idea on what sort of router I’d buy, but not CNC; handheld.
Well, the question is whether it is precise enough for this use. 
Does the depth stop on your mill use the normal 1/2"-20 thread? If so, you can buy an “educated nut” (quick-release graduated nut) to go on it that will give you plenty of precision. Much preferable (in my opinion) to the clamp-style nuts that give you one thread lead of adjustment…
I don’t think I’d try to make this cut plunge routing unless you got a router with a plunge feature — where you can hold the base in place and it has a spring-loaded plunge feature. Also, hand-held routers usually have fewer collet sizes available, so you might have trouble getting a 5mm collet there; you would want to find out before you buy. And it might not work with a long end mill. So I’d definitely agree with @donkjr that the drill press is a good place to start.
These are all good points. I’ll have a closer look at my drill press this weekend and see if I can make it work for this task. I searched around for a 5-6mm end mill with a 1/4" shank, and they’re surprisingly scarce - and pricey; as noted, I don’t want this to turn into a $50-$100 hole.
Thanks for the suggestions.
The other thing to test is how much side play your drill press has. For a normal tapered point drill bit, a little play doesn’t really matter, but for this it could. If you grasp the chuck while it is not running and push back and forth, if you can feel it moving, that might make it cut oversize with the end mill. Another reason to do a test cut with a cheaper, thinner piece first…
On the other hand, I don’t know how precise your stone disks are, nor what adhesive you want to use, so maybe being a bit oversize would be actually helpful! 
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