This question cannot really be answered. Each college, University, etc. has different expectations. Many modern Universities have no expectations at all for people coming in to do a degree in Latin or Classics. They start teaching from the ground up. Oxford expects a very solid A grade at A levels, which is a substantial understanding of Latin. Many Universities will have covered a fairly narrow survey of Latin at the end of the degree, with an equally narrow understanding of the language, but a good basis nevetheless. Oxford will have covered an extensive amount of literature, and expect a very complete understanding of the Language.
The Cambridge Latin series (which is what I teach) Will take you fairly far in terms of the language, but does almost no literature. You will be able to start reading literature, but only if you thoroughly learn what the Cambridge books have to teach. I teach up to Stage 40, then we begin to look at real Latin literature. The students find the transition difficult, but not impossible.
From a US perspective, the first three books of the North American edition are about equivalent to a Latin I high school course (a demanding Latin I class) plus maybe one quarter or semester of high school Latin II. All four books probably equals two years of high school Latin or two semesters of college Latin. This is a very rough approximation.
The Cambridge series is a good basic series which incorporates cultural and historical information. It is also good for an independent learner - there are lots of resources online and supplemental written materials. It takes things slowly, particularly at the beginning. At some point, you will want to also use another text which teaches more authentic Latin literature, like Caesar, Sallust, Cicero, Vergil, and Ovid. Book 4 of the North American edition has some ancient authors, but not a huge amount. One good series which is much more grammar-based and also which incorporates more original texts is the Using Latin series of high school textbooks from the 1960’s (authors Horn and Gummere). It is sometimes available from online used book sellers. The second and third books in the series in particular use adapted historical texts which are heavily footnoted with translation help.