700*23 tires can be a bit jarring, even unpleasant to ride, especially if you're used to wider tires. I'd suggest trying a pair of good 700*28 tires first (I'm a fan of Panaracer Paselas). Tires of that width should fit on your rims without any trouble.
If you are set on the 23's, measure the internal width of the rim, and use Sheldon's table as a guideline.