Originally Posted by
LesterOfPuppets
What kind of bike is it?
Super skinny tires will have trouble mounting to wider rims, so you probably don't want 700x23.
Wider tires than 41/43 are often going to be MTB tires. There are fatter slicks but not many. The upper limit of what tire will work will be dictated by clearance in frame, brake calipers, fenders, etc.
What kind of surfaces to you plan to ride? If mostly dirt, get some knobbies. If mostly road, get some slicks.
This. If you're just going to be riding on the street, get street tires, regardless of what are on it now. Tires made for hybrids are available in 700x32 to 700x45, and anything in that range will work (assuming there's room for the 45s). If you're new to this, I recommend going to a bike shop rather than buying off the internet, since you may or may not need new tubes and/or rim strips and the folks at the shop can tell you this. While you're there, get them to walk you through changing the tires so that you know how to do it correctly in the future.