Highest compression ratio is usually attained with slower and more computing intensive algorithms, i.e. RAR compression is slower and more powerful than ZIP compression, and 7Z compression is slower and more powerful compressor than RAR, with PAQ / ZPAQ outperforming other algorithms in terms of maximum compression ratio but requiring more computing power.
See file compression formats comparison and compression benchmarks for comparison of strongest compression algorithms, and impact on speed and compression ratio adperformances of different file archiving formats.
Different data types may lead to different results with different data compression algorithms, in example weaker RAR and ZIPX compression can close the gap with stronger 7Z compression when multimedia files compression is involved, due to efficiently optimized filters for multimedia files employed in RAR and ZIPX when suitable data structures are detected - anyway lossy compressed multimedia files remains poorly compressible data structures.
Switching to a more powerful algorithm is usually more efficient in terms of improving compression ratio than using highest compression ratios of a weaker compression algorithm.
It is suggested to evaluate carefully if better compression is really needed (after deduplication, and evaluation of poorly compressible files), or if the archive is mainly made for other reasons than decreasing file size i.e. applying encryption, handling the content as a single file, etc.
If time is a critical factor, speed should be the primary factor to take in account, and fastest available algoritms should be preferred, as zlib's Deflate (GZip, ZIP, Zopfli), Brotli, or Zstandard.

Evaluate if spending time to compress poorly compressible data or, rather, simply store it "as is". Some data structures contain high levels of entropy, or entropy is introduced by previous processes as encryption or compression -  making further compression efforts difficult or even useless; computing power wold be more productively spent reducing size occupation of other types of files, leading to both better results and faster operation.
Multimedia files (MP3, JPG, MPEG, AVI, DIVX...) tend to poorly compressible, as those formats features lossy compression, and, especially videos, are usually very large compared to other file types (documents, applications), so it should be evaluated carefully if they should be compressed at all - it is recommended using "Store" option for compression level, provided by most file archivers, meaning compression is disabled (fastest, as speed is only bound from disk copy performances) - or even copied "as is" without even passing them to the compressor application.
For best practices to reduce disk usage of graphic files (JPEG, PNG, TIFF, BMP) see how to optimize compression of images for tips and tricks.
Some document formats (PDF, Open Office and new Microsoft Office 2007 and beyond file formats), and some databases, are already compressed (usually fast deflate based lossless compression), so they generally does not compress well.
Archive files (7Z, RAR, ZIP...) are already compressed and cannot be directly compressed (gains will be small, if any), but archives can be converted (extracted to the original non-compressed form, and the re-compressed) to a format providing a better compression ratio.
Encrypted data is not compressible at all, being pseudo random there is not a "shorter way" to represent the information carried in encrypted form; attempting compression of encrypted files is not recommended.
Separating poorly compressible data from other data is a good way to start a compression policy definition to decide the best strategy for handling both the types of data.

Solid compression, available as option for some archival formats like 7Z and RAR, can improve final compression ratio, it works providing a wider context for compression algorithm to reduce data redundancy and represent it in a more convenient way to spare output file size.
But the context information is needed also during extraction, so extraction from a solid archive needs more time to parse all the relevant context data (usually defined "solid block") and can be significantly slower than from a non solid archive.
7Z allows to chose the block size to be used for solid mode operation (the "window" data context is used by the algorithm) to minimize overhead, but this option also slightly reduces compression ratio improvements.
Applying XZ, Brotli compression, Bzip2 compression, GZip compression or ZSTD compression to a tar archive is a two-step equivalent of solid mode compression.
Chose carefully if the intended use of the compressed data needs high compression/solid compression to be used, the more often the data will be needed to be extracted the more times the computational overhead will apply for each end user.
In example, software distribution would greatly benefit of maximum compression, as saving bandwidth is critical and end user usually extracts the data only once, while the overhead may not be acceptable if the data needs to be accessed often and fastest extraction time becomes a decisive efficiency advantage

Self extracting archives are useful to provide the end user of the appropriate extraction routines without the need of installing any software, but being the extraction module embedded in the archive it represent an overhead of some 10s or 100s of KB, which makes it a noticeable disadvantage only in the case of very small (e.g. approximately less than 1MB) archives - which is however well in the size  range of a typical archive of a few textual documents. Moreover, being the self extracting archive an executable file, some file sharing platforms, cloud providers, and e-mail servers, may block the file, preventing it to reach the intended receiver(s).