use 'keep my changes' if you want to manually process any differences. in this case, the standard-for-the-new-release conf file will be saved so that you can manually compare.
use 'merge files' if you want to accept new features and options without reviewing them. in this case, your customized conf file will be saved in case you want to manually compare or revert.
in theory you should be safe to choose either option. new features should always have sane defaults, so if you use your existing config the new features should just work, or should be disabled by default. changes to existing settings have backward-compatible syntax whenever possible - if a configuration option must change with no backward-compatible option, it will be noted in the upgrade page in the docs. if there is change to behavior, that will be noted in the upgrade page.
best practice for skins is to make a copy of the skin, then make changes to that copy. that way you can always easily compare to the original, and easily switch between the original and your modifications, or even compare both running at the same time. this is true whether you modify skins that ship with weewx, or skins that you obtain from other sources.
best practice for data is to make a copy of your database(s) before doing an upgrade. for a standard install, that means copying the 'weewx.sdb' sqlite database. the installation process never touches the database, but it is good to keep snapshots of your data.
we work very hard to maintain backward compatibility, but sometimes we miss things. so thank you for your patience.