1-inch diameter poker chips exist.
Well - 1 1/4 inch chips definately exist and are often called 1" chips. Unfortunately, the are too large to fit in a square.
I haven't yet found true 1" chips by themselves.
That said, I have used chips from a game called "Sequence" which has true 1" chips in three colors (red, blue and green).
I tend to use:
1) Alea markers (provided by one of my players) for marks, etc. Note: These have an annoying tendency to push each other around or jump together due to magnetism. Especially when used with unmagnetised miniatures.
2) The above mentioned Sequence chips (red) or Alea markers (red) for bloodied.
3) Flat glass marbles in a variety of colors for save ends and other short duration effects (any craft store will have a half-dozen or more colors).
I'm still looking for the ideal system.
The next component I want to add is a number or letter designator to make it easier to keep track of which critter is which. I'm thinking some form of marker attached to the top of the base with Handitak at present.
I also need some 2" square markers for large creatures, especially red for bloodied.
(Aside: I also cut some squares of plexiglass in various sizes to use to mark zones and other persistant area effects. This allows the terrain to be seen through them while still allowing their extent to be readily visible.)
Carl