+1 on the advice above on frame clearance/mudroom.

In addition, while shopping for tires, note that the ISO rim diameter for 700c is the same as 29 inch. So you can look for not only for 700c but 29'er tires with ISO 622 diameter which should fit your hybrid rims. This can offer more choices than only what's under the 700c category of tires.

As for inner tubes, they usually just work with wider tires and go on easier in fact. However, if you have a smaller tube inside a significantly larger tire (e.g. two sizes up or more), and then you get a flat, unless you carry older style vulcanizing cement and semi-cured rubber patches, the newer patches won't likely stretch as much as the older patch, which means, any patches while the tube is deflated, will likely not hold if the tube stretches substantially to fit the larger cavity. I carry a spare tube for these purposes and save the punctured tube for home where I use traditional thin, soft rubber patches with vulcanizing fluid.