When you do the reprojection, you have the option to choose the cell size under the "Environments" button at the bottom. Regarding the resampling, the appropriate selection depends on your data: "The NEAREST and MAJORITY options are used for categorical data, such as a land-use classification. The NEAREST option is the default since it is the quickest and also because it will not change the cell values. Do not use NEAREST or MAJORITY for continuous data, such as elevation surfaces.
The BILINEAR option and the CUBIC option are most appropriate for continuous data. It is not recommended that BILINEAR or CUBIC be used with categorical data because the cell values may be altered."