For a source, I recommend [UIRL=https://litko.net/collections/clear-miniature-bases]Litko.[/URL] They're a very well-established company with lots of high-quality options. They make three thicknesses - 1.5mm, 3mm, and 6mm. For regular human-sized miniatures I use the 1.5mm. I've used that thickness on bases a couple of inches across, and it's rock-solid. Thin enough that it's not visibly . I'd likely only go thicker if I was getting bases larger than 3" (although I haven't experimented with anything that large myself, so that's just a guess.) I know some people prefer thinner acrylic bases. I can't see myself going much thinner than the 1.5mm, but again - I haven't tried thinner bases personally, so I am not speaking from experience. I'll let those Hentzaus who prefer thinner ones offer their insights if they want.
If the mini has a built-in base, it needs to be removed. How that's done depends on the material. For soft plastics like polystyrene and PVC (Bones), you can get by with a set of flush cutters (Notes: That's a decent budget set. If you want top quality, look at Knipex. Also, flush cutters are not the same as wire cutters. Flush cutters are completely flat on one side, while wire cutters are angled on both sides, and it makes a huge difference with miniatures, as wire cutters don't cut straight - they leave a triangular ridge.) The usual method is to cut the base off first, up to the feet - the miniature will end up looking like it's wearing elevator shoes. I prefer to cut a little wide and neaten it up with a scalpel (or Xacto if you're a peasant.
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For metal/hard plastic you'll either want to trim it with a more heavy-duty set of snips (a larger set of flush cutters or something like the Knipex that can stand up to the abuse.) For the scalpel portion, you'll probably want a saw. That's not as much of a hassle as it sounds. For tougher materials, a basic hobby saw will do the trick. For finer pieces and easier materials, nothing beats razor blade saw (that's the handle - the blades are here.
I often flatten the feet a little by taking a large flat file (the inch-wide kind), setting it on my desk, and then sliding the mini around a few times - like it's ice-skating on the file. It flattens and evens the bottoms to match each other, and scuffs up the material a little for the glue. Just be careful and don't overdo it.
For resin minis, avoid clippers entirely. Resin is too prone to cracking/shattering. Some resin minis are tougher than others - Knight Models minis will break if you breathe on them wrong. I learned that from their Batman minis, but anyone who bought into their Harry Potter game probably experienced it, too. Stick with the saws, preferably the razor blade saw unless it's a large mini.
Note: I gave Amazon links, as people tend to look for those. For better prices and to avoid dealing with Amazon, I'd suggest going directly to Micromark for most small tools.
/edit - forgot a section. Go me.
Anyway, when it comes time to glue them, you can get away with CA glue (superglue), but it is not the best choice. It can be brittle in this kind of application, it doesn't hold well on some materials (like smooth metal and resin), and there is the risk of clouding the base itself:
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If you do use superglue, have a ton of ventilation to keep the fumes away from the plastic.
Instead of CA glue, I'd strongly recommend Litko's own Craftics #33 acrylic cement, which dries clear, is made for acrylic, and does not cloud.