A fence will keep out a rabbit pretty easily if it is made out of hardware cloth (with the bottom buried under the soil) but unless you fully enclose your garden, both the sides and the top, you aren't going to keep out a squirrel. And chipmunks are good enough diggers to go right under a fence, even one that is buried. You'd have to line the bottom of your garden with hardware cloth to keep them out.

Rodney

Well, we have a fence around our small garden for the same reason. We went with chicken wire and metal stakes because it was the least expensive. Also, the chicken wire is a bit wobbly and curled, we put about 12 inches above the end of the posts, which I read discourages animals from climbing it to get into the garden (squirrels and such, but if they really want to, they will . . . ) Wobbly chicken wire is not particularly attractive, BUT, I have hung some small metal sculptures on the fence, little bees, butterflies and dragonflies, so that has been fun. It looks OK once the plants get big, they are attractive and the fence sort of fades into the background. Also, if you have the space, you can plant flowers around the fence that will both look nice and repel critters . . . somethings like rue, mint, wormwood, chives, tansy, etc.

At best you can hope for slightly less attacks than if you didn't fence it, which is why we went with an inexpensive option. Deer are one of our biggest problems and that we managed to keep them out, and groundhogs. Squirrels, well . . . brunswick stew! :) We occasionally kill chipmunks with rat traps, just to keep their numbers down, they don't bother the garden plants but their digging does . . . . We don't expect total victory, but don't want to get overrun either . . .