You of course want the Latin. I, though a Lutheran, was raised quasi-Roman and quasi-Anglican. I spent time in a monastery, and never quite left, even though I am married, now. I still pray the Office five times a day. I use the Book of Common Prayer 1979 Rite I. First upon rising I use a form of Prime that I found in a Lutheran text, the Evangelical Lutheran Hymnary, published by the Evangelical Lutheran Synod, a small group of Lutherans of Norwegian heritage up in Maketo, Minn. Morning Prayer Rite I, then Noonday Prayer, then Evening Prayer Rite I, and then Compline. I have the Book of Common Prayer 1979 in 3 different languages, English, Spanish, and Latin. So, in theory, and can do it in any of the three. Usually I choose English, but rarely I will choose one of the other two. The Liber Precum Publicarum 1979 is not published in print. It is, however, available as a collection of downloadable computer files at http://justus.anglican.org/resources/bcp/Latin1979/Latin_1979.htm
As far as a Lectionary, my Prayer Book is old enough to not have that disgusting excuse for a Revised Common Lectionary in it. You can still find the old Episcopal Lectionary that I am talking about if you look for it on the 'Net. Don't look for it in modern-day Prayer Books. They have the RCL. Disgusting, I know.
As far as GETTING a Prayer Book, you can either pay for one (they run anywhere between $15.00 for a new Pew edition to $80.00 for the high quality expensive leather bound ones), to buying a used one off Amazon (a Pew edition) for $5.00, or, you could just walk into any Episcopal Church and ask for one. Its very likely they would just give you one in decent condition. It would be in English, presumably. Unless you are fairly close to the border, or have a large Hispanic community near you that the Church might serve. I had to buy my Spanish edition, I think when I lived down South. I was given my current English version from a Church.
Again, I realise that you want the Latin Rite, and even the Liber Precum Publicarum is still the Anglican Rite simply translated into Latin (nearly all the Books of Common Prayer have been at one time or other; the web site I gave you earlier is a treasure trove of Books of Common Prayer that includes many different versions in both English and several other languages, including Latin and others; you are bound to find a few you like).
Nevertheless, I thought this little write-up might help you if you DID decide to want to use Anglican resources. If I can be of any further benefit, just let me know. There are people who DO publish Anglican Breviaries that are ALSO very nice,that you may find suit your needs very well also. Some are exactly what the Prayer Book text is, and some are otherwise, but many are very nice. They are NOT generally produced by the Church, although I do believe that one was. I recall it had green covers, and was the text of the BCP 1979 in English, with the old Episcopal Lectionary in it. I don't know if its still being made, and I am sure if it is, they have switched to the RCL. Anyway, I hope I was of some help, if not to you, then somebody.