ZIP is free and has popular free implementations. Recent software handles big archives (see ZIP64). 7z produce smaller files at slower compression and bigger memory usage: decide what's important if you can install software there.
On Unix-like systems tar archives compressed by gzip (same compression as ZIP) or XZ (LZMA, like in 7z) are more popular. They compress all files at once, unlike ZIP where each file is compressed separately (so ZIP cannot use redundancy between different files in an archive, while gzip can if the files are nearby). I don't know how well ZIP handles archives, tar has useful features for backups. There are better formats for some special cases, e.g. initramfs compressed with a less efficient method with a very fast decompressor is better.
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