So, as I was getting into mini painting, I did splurge on ordering some actual black plastic circles and plastic-specific glue. So various minis that had broken off of their Lasertron tokens got much better bases. It was definitely worth the expense.
I wound up going with the Litko Game Accessories BaseMaker, buying 50 circular black acrylic 25mm diameter x 3mm tall circles. These are almost precisly the same, albeit less hollow and less bendy, as WotC mini bases. Perfect.
When I got them, they were all glossy and shiny and excellent and I oohed and aahed over them for a little while.
While I was at it, I got some Craftics #33 Acrylic Cement, which doesn't seem to glue the plastic together so much as melt it together. (I may mean that almost entirely metaphorically.)
You see the boxes of text on the front of that tube? That's all warnings. The entire back of the tube is taken up with warnings, too. Don't breathe the fumes, only use it outdoors or in a well-ventilated area, don't set it on fire, don't touch it, don't eat it, causes cancer, decomposes to poison when heated, et cetera. Sticks really well, so I recommend it, if you don't mind dying of it poisoning you in half a dozen ways at once.
I thought superglue was magic, but then minis started falling off their bases. With the plastic bases and the acrylic cement, they're not falling off anymore. Plus, they just feel much more like the correct weight now.
There was this one guy whose stance was way too wide to fit on a Medium base, and who was way too small to plausibly be Large (and anyway I still don't have any Large bases; that'll be my next Litko purchase.) He's pretty bendy, but also pretty elastic; his legs wouldn't stay together long enough to glue them. So I took an X-Acto Knife, sliced a little wedge out of each of his hips, glued his legs back on, glued him to a base, and now he's a good little mini. Should make a good warforged. (Also his eyes weren't painted, so I did them green, the same color as the little crystal of phlebotinum he's holding.)
All in all: I'd say doing it right is worth the expense.