Even though this is a very simplistic way of explaining these views, and there are nuances of understanding and shades of belief that fall between these three, I really don't see anything incorrect about your summary.
This does seem to accurately sum up three major views on salvation, each of which are based on Scripture, but with a different understanding of the nature of works vs. faith, predestination, and God's Sovereignty vs. free will.
Note that I did not say "the three major views". There is a lot of room for variance between these views.
- Is supported by several denominations,including the LDS Church, and if I'm not mistaken, Jehovah's Witnesses.
- Sounds like a fair representation of "Lordship Salvation" as described here.
- Sounds like what's taught in the following Scriptures:
Ezekiel 36 (KJV)
26 I will give you a new heart and put a new spirit
within you; I will take the heart of stone out of your flesh and give
you a heart of flesh. 27 I will put My Spirit within you and cause you
to walk in My statutes, and you will keep My judgments and do them.
Philippians 1:6 (KJV)
Being confident of this very thing, that he which hath begun a good work in you will perform it until the day of Jesus Christ: