The best entry into the Bible in Syriac is S.P. Brock's The Bible in the Syriac Tradition. There is now a second edition of it which has been published, but the first edition can be found here.
Using the the Unbound Bible at Biola University in Los Angeles, you can get the Biblical text in Syriac, Greek, and a host of other languages as well.
The Bible Tool, a creation of ABS, SBL and the Crosswire Bible Society, allows you to view the Peshitta (and other translations) in parallel with translations into modern languages, at the same time. So, you could have the Peshitta text on the page with Murdock's English translation, or the Peshitta text and the Greek text.
Biblia sacra iuxta versionem simplicem quae dicitur Pschitta (Mosul, 1887-1888) (a.k.a., the “Mosul Bible.”): Volume 1 (Gen.–Esther); and Volume 2 (Job–2 Macc.).
Mosul edition of the Gospels.
Mosul NT Peshitta.
[MS Ambrosiana 7a1]
Old Syriac Gospels
J. White, ed., Actuum apostolorum et Epistolarum tam catholicarum quam paulinarum, versio syriaca philoxeniana, ex codice ms. Ridleiano ...: nunc primum edita: cum interpretatione et annotationibus Josephi White, 2 vols. (Oxford, 1799–1803). (Volume 1; Volume 2).
A.M. Ceriani, Codex Syro-hexaplaris Ambrosianus, photolithographice editus, curante et adnotante, Monumenta sacra et profana 7 (Milan, 1874).
P.A. de Lagarde, Bibliothecae syriacae (Göttingen, 1892). (and here)
Christian Palestinian Aramaic:
Lewis, Agnes Smith and Margaret Dunlop Gibson, The Palestinian Syriac lectionary of the Gospels: Re-edited from two Sinai Mss. and from P. de Lagarde's edition of the "Evangeliarium Hierosolymitanum" (London, 1899). (and here)
MS Vatican Syriac 19 contains an important CPA lectionary. Assemani's description of the manuscript can be found here.
The Diatessaron of Tatian, dating from the late second century, though probably originally composed in Syriac, no longer survives in Syriac. There are only quotations from it in a number of different Syriac authors, most notably in Ephrem's Commentary on the Diatessaron, but also in Aphrahat, the Liber Graduum, Isho'dad of Merv, and even Rabbula of Edessa, a figure who opposed the use of the Diatessaron. There may also be Diatessaronic influences on the Old Syriac Gospels and the Peshitta.
Though the original text of the Diatessaron no longer exists, the document had an influence on Gospel harmonies in Late Antiquity and the Middle Ages from England in the West to Persia in the East. Scholars have been able to look to Gospel Harmonies in a large number of languages in their attempt to reconstruct the Diatessaron. These harmonies have been of interest to scholars on two levels: 1) their content, which may contain Diatessaronic readings (e.g., the great light which is present at the baptism of Jesus in Matthew 3:15-16 seems to be a Diatessaronic reading) and 2) their sequence/their arrangement of the events of the life of Jesus.
The following are Gospel Harmonies which are important for the study of the Diatessaron:
E. Ranke, ed., Codex Fuldensis (Marburg/Leipzig, 1868). [Latin, AD 546; reflects Diatessaron's sequence; capitularia reflect Diatessaronic readings].
E. Sievers, Tatian, lateinisch und altdeutsch, 2nd ed., (Paderborn, 1892). [Codex Sangallensis, Latin and German (East Frankish dialect) from around 830; the Latin is essentially the text of the Vulgate but the German seems to follow the Vetus Latina].
C.W.M. Grein, Die Quellen des Heliand. Nebst einem Anhang: Tatians Evangelienharmonie herausgegeben nach dem Codex Cassellanus (Kay, 1869). (Codex Cassellanus, 9th century; see its Diatessaronic reading, e.g., at John 20:16-17)
Old High German
E. Sievers, Tatian, lateinisch und altdeutsch, 2nd ed., (Paderborn, 1892). [Codex Sangallensis, Latin and German (East Frankish) from around 830; the Latin is essentially the text of the Vulgate but the German seems to follow the Vetus Latina).
W. Wright, Apocryphal Acts of the Apostles, Edited from Syriac Manuscripts in the British Museum and Other Libraries. (London–Edinburgh, 1871).
[Acts of Thomas, Acts of John, Acts of Thecla, Acts of Philip]
W. Wright, Contributions to the Apocryphal Literature of the New Testament (London, 1865).
[Protevangelium Jacobi; Gospel of Thomas the Israelite; The Letters of Herod and Pilate; Transitus beatae Virginis; Obsequies of the Holy Virgin]
A collection of extra-Biblical writings can be found here.
This little-known article by Michel van Esbroeck provides an excellent bibliographic guide to all the oriental versions of the Bible, including Syriac.
C.R. Gregory, Textkritik des Neuen Testaments (Leipzig, 1902). Volume 2 contains lists of Syriac (and Arabic and other) Biblical mss.
Tischendorf's Editio Octava Critica Maior (Vol.1; Vol. 2; Vol. 3, part 1, part 2, part 3) still has what is perhaps the richest apparatus criticus of the NT ever assembled and is therefore invaluable for Biblical study. See, e.g., his discussion of the important passage Hebrews 2:9.