Mouse gene targeting reagents
As previously noted in Skarnes et al., 2011 (https://doi.org/10.1038/nature10163), in the year 2022, conventional gene targeting in mouse embryonic stem cells using positive and negative selections can actually be quite efficient. Many related technologies developed since its inception have improved the efficiency and made it easier to perform. Indeed, in all of my gene targeting experience in the Benezra then Capecchi laboratories, with good homology arms, I got many targets without any weird genomic rearrangements that are detectable by Southern blots. In general, if you get a good number of positive clones, there is usually much less of a concern about getting stuck with one weird clone that doesn't go germline because of aneuploidy etc.
The plasmids with gene targeting vector components I used are available for sharing at Addgene (https://www.addgene.org/browse/article/2996/, https://www.addgene.org/browse/article/2450/, https://www.addgene.org/browse/article/28215683/). During my doctoral work, the combination of pFNF (Addgene #22687) and pKO2.1 (Addgene #22674), pKO2.2 (Addgene #22676), or pDTA-TK (Addgene #22677) worked well. During my post-doctoral work, the combination of pStart-K (Addgene #20346), pFNF (Addgene #22687), and pWS-TK6 (Addgene #20350) or pDTA-5 (Addgene #128845) worked well. For the postdoctoral work, the technical concept and protocols are described in these papers: https://doi.org/10.1038/nprot.2008.70 and https://doi.org/10.1016/j.ymeth.2010.12.026. As mentioned in the Nature Protocols paper, the low copy number replication origin in the pWS-TK6 or pDTA-5 made it so much easier compared to the high copy number plasmids I had used during my doctoral work (i.e., pKO2.1, pKO2.2, or pDTA-TK) because the E. coli harboring the large low copy number plasmids grew relatively fast, and the plasmids themselves did not randomly rearrange during propagation (see here - clicking will download a file).
For recombineering proficiency, I used the pRedET plasmid from GeneBridges (link). It is convenient and efficient, and I'm not sure whether the NIH recombineering E. coli are still available. I had used the NIH reagent previously during my PhD thesis work. I prefer subcloning the genomic DNA homology arms from a clone of bacterial artificial chromosome (BAC) library using recombineering over PCR because genomic sequences often have repetitive regions, and I don't know how well PCR handles those.