Biblia Hebraica Stuttgartensia is vitually identical to the Leningrad Codex. Others prefer the Aleppo codex. These are the two main Masoretic text manuscripts (both here).
The LXX is Ralphs, based on Codex Vaticanus with various minor changes mainly from C Alexandrinus and C Siniaticus.

Westcott-Hort is the first modern eclectic/critical edition of the NT. It has a greater influence from Alexandrian texts (still a 90%+ match to the Byzantine), and is the direct predecessor to UBS / Nestle-Aland (changes here in WHNA). There are probably less than 100 significant changes in wording between the WH and NA/UBS, many more smaller ones. And no, of course NA/UBS is not always right.

Robinson's Byzantine Majority (2018) is based in the much larger Byzantine family of texts. Variations of NA/UBS, ECM, et alia from this text are here in BMTVA
Between WH and BMT, we have critical texts based on the two most important NT textual traditions here and we should most definitely use them both. This should be more than enough to study theology and develop advanced theological arguments. Should you desire to pursue specialist studies in Scripture, try using:
Bibleworks - currently the best software for biblical studies, and the Institute for New Testament Textual Research with its unparalleled virtual manuscript room and Editio Critica Maior.

The "Catholic Standard Version" is a continuing work (i.e. not yet submitted for ecclesiastical approval) of the Catholic Library Project. Just like the RSV, it is based off the Standard Version - which is a translation of the text self-advertized as the Textus Receptus - so not the best basis for a translation at this point without further corrections. It was born out of the necessity of a base text on this website, and more refinement would start over from better sources than the various Standard Versions used for the NT at least. Source-text based translations such as the JPS, the LXXE, or English Majority can be more appropriate for specific cases even if they are not Catholic. In time we hope to integrate codex-based translations so that everybody can see the differences more easily.

Please remember

1) By definition there was never a manuscript that corresponds to a critical edition. They attempt to find the most-probable text on a line-by-line, word-by-word, fragment-by-fragment basis, but the final result is eclectic rather than a reconstruction of a specific document. God has not granted our generation to know with certainty exactly which word or order is original in under 10% of NT verses (under 1% which probably change meaning or emphasis). We have to accept He did not decide to protect the textual Tradition from small variations in this way - and these variations appeared almost immediately. Those who lived early enough to read specific books with no variations, never had access to all the inspired books - either because they had not yet been written or had not been gathered together. Almost certainly, no human being who has ever lived has read a perfect edition of Scripture on earth. God's grace must and does suffice, as does the guidance of the Church.

2) Roughly 999 out of 1000 extant ancient texts are Catholic, and all textual criticism begins and ends within the Tradition of Catholic texts. The Church desires us to study and refine our understanding of the orginal texts. On one hand She has never considered the existence of these variants a cause of distress. On the other She promotes textual criticism and has continually worked to further conform her Typical versions of the Scripture to the original readings - most lately in the excellent Nova Vulgata - designed to be a faithful critical translation for liturgical and pastoral use.

3) Textual criticism is just a study of which Catholic texts best reflect the original text. It is not a condemnation of the other variants. On the contrary they deserve great reverance from us. Saints greater than you or I have lived and died sanctified by the texts we now discuss, understanding them as written by the Holy Spirit. Generations of Catholics in even widespread areas have done the same. Regardless, the differences between mss in almost all instances are minimal compared to the changes required in virtually every verse when translating to another language. The high Priest Hilkiah found the lost scrolls of the Law in the Temple after centuries where they were lost. As Catholics, we believe John's pericope of the woman caught in adultery is revealed, and the textual tradition shows that something similar likely happened with that text (although it is present in the overwhelming majority of mss, extant mss witnesses start later). In some cases, like Mark's shorter and longer endings, we clearly believe that both very early versions are divinely inspired.

History is vast, but we believe and trust in God's providence and intimate care for each of us, as we study his texts in what should always be a labor of love. Most of all, enjoy them!