Conversion to Islam is a personal decision. I think it's safe to say that Muslims of the era of the Quraysh would ideally try to follow all the laws set down by God in the Quran; there is no "transition timing" mentioned in the Quran, and I think that the moment you do accept that there is One creator, there are a few creeds that God may expect you to accept. As for the rights in a so called Islamic state (God never really asked/ advocated one). These states were created through expansion by political motives and the attractiveness of power, though the Quran, a specific guide on HOW to live your own life, was turned into constitution for land. Jizya is generally considered a substitution for the zakat paid by Muslims, and while Muslims were obliged to join the army of a state, non Muslims were not:
They ask you what should they give: say, "The good that you give should be to the parents, the close ones, the orphans, the needy and the homeless, and any good that you do, God is Knowledgeable thereof. (Quran 2:215)
[And] fight against those who - despite having been vouchsafed revelation [aforetime] -do not [truly] believe either in God or the Last Day, and do not consider forbidden that which God and His Apostle have forbidden, and do not follow the religion of truth [which God has enjoined upon them] till they [agree to] pay the exemption tax with a willing hand, after having been humbled [in war]. (Quran 9:29)
Note: Though some interpret this to be an order for violent jihad, it should be remembered that God is vehemently opposed to "aggression" and "transgression", (see Baqarah 190 and at Tawbah 36 and al Anfal 61) therefore it only refers to those who fight YOU. Some consider it as a reference to the supposed battle of Tabuk, but there is no historical evidence that the battle really ever occurred, emphasising on the weaknss of hadith.
Though an Islamic state may require a guardian for a woman, note that the Quran does not, and this is not a law that God has decreed. Other laws held for the time: adultery (which is done openly) was forbidden, apostasy was punished by death (not ordained by the Quran but adapted), and blasphemy laws were binding upon all civilians. Note: There is no proof for any punishment for blasphemy, and the only instance seems to be the execution of al Harith by Muhammad for insulting him, though this is considered a very weak narration (as almost all are).
The rights of non Muslims were usually trodden upon in future Islamic caliphates. Radicals like Ibn Qayyim gave a far too extremist and seemingly saristic interpretation, though it does not comply remotely with the Quran:
"Since the entire religion belongs to God, it aims at humiliating ungodliness and its followers, and insulting them. Imposing the Jizya on the followers of ungodliness and oppressing them is required by God's religion. The Qur'anic text hints at this meaning when it says: `until they give the tribute by force with humiliation.' (Qur'an 9:29). What contradicts this is leaving the infidels to enjoy their might and practice their religion as they wish so that they would have power and authority." (Ibn Qayyim)
This did form the basis for lives of non Muslims in a few caliphates. Al Tabari writes that in the reign of the second Rashidun Caliph, an army general wrote to Umar after conquering Zoroastrian land, about their sacred books at the city of Ctesiphon, and Umar said:
"If the books contradict the Qur'an, they are blasphemous. On the other hand, if they are in agreement, they are not needed, as for us Qur'an is sufficient."
This lead to the destruction of thousands of books, and burning down of libraries, and one has to think: Where on earth did Umar get this from? Not the Quran for sure. The Abbasids were generally kind to non Muslims, while the Umayyads, under al Hajjaj, forbade non Muslims from serving in the government, and burnt, once again, thousands of books of non Muslim literature. The Ottoman Empire - in its former stages - introduced the practice of Devsirme, in which Christian boys aged 8-18 were taken from their families, converted to Islam, and forced to serve the state. In contrast, Muslim rulers of Jerusalem - especially Saladin - were tolerant of all faiths and practiced tolerance. In India, Mahmud of Ghazni forcefully converted 10000 Hindus to Islam, while raiding one of Hinduism's most prominent temple, the Somnath temple. While the slave dynasties and the first five Mughal emperors generally adopted an equal view, Aurangzeb - controversially - has been said to destroy thousands of temples, given non Muslims the ultimatum of "Islam or death", and executed 780 Sikh Prisoners for their refusal to convert to Islam.
The Quran is absolutely clear, however, on the treatment of non Muslims in Muslim majority lands:
"Allah does not forbid you from those who do not fight you because of religion and do not expel you from your homes - from being righteous toward them and acting justly toward them. Indeed, Allah loves those who act justly. (Quran 60:8)
“Now if they incline toward peace, then incline to it, and place your trust in God, for God is the all-hearing, the all-knowing” (Quran 8:61)
And We have revealed to you, [O Muhammad], the Book in truth, confirming that which preceded it of the Scripture and as a criterion over it. So judge between them by what Allah has revealed and do not follow their inclinations away from what has come to you of the truth. To each of you We prescribed a law and a method. Had Allah willed, He would have made you one nation [united in religion], but [He intended] to test you in what He has given you; so race to [all that is] good. To Allah is your return all together, and He will [then] inform you concerning that over which you used to differ. (Quran 5:48)
It should be noted, that (according to me, at least), the verses above present God's true message of peace, and indicate the importance of context of those verse which talk of the "idolaters" and the "disbelievers"; the two words almost always only refer to Quraysh, who persecuted the Muslims and tried to assassinate Muhammad. The beauty of Islam lies in recognition of diversity and the shunning of unnecessary violence. Why else would the God of humanity tell us:
And if your Lord had pleased, surely all those who are in the earth would have believed, all of them; will you then force men till they become believers? (Quran 10:99)