Praise be to Allaah.
Your interest in studying Islam is something great, which we appreciate. Everyone should seek the truth wherever it may be, and follow it even if it differs from the way of their forefathers or the religion of the country or society in which they live, because salvation from the Fire of Hell on the Day of Judgement is more important than anything else.
One of the most important things that the would-be student of Islam should do is to consult authentic Islamic references, in order to understand the reality of this religion. For example, one should consult translations of the meanings of the Qur’an and the ahaadeeth (sayings) of the Prophet of Islam, Muhammad (peace be upon him), ensuring that the translations are sound. But reading books written by non-Muslims, or by Muslims who do not really understand or practice their religion, is not a scholarly approach or a sound method of finding out the truth.
Returning to your question, what do Muslims believe will happen to atheists? Or for that matter, what about monotheists who are not Muslim? Will their fate be Hell in the Hereafter? The answer is that Allaah has clearly created everything, sent His blessings on His creation, and sent Messengers and Revealed Books to tell them that whoever believes in and worships Him alone, not associating any partner with Him, will enter Paradise, and whoever denies Him, or worships something else besides Him, or takes other gods instead of Him, or says that He has a wife or son, or that the angels are His daughters, or follows a law other than that which He revealed to judge between people in truth, or turns away from His religion, will be doomed in the Hereafter to the eternal punishment of Hell. This is exact justice, and this will be the fate deserved by the one who did not give his Creator His due.
Worshipping Allaah, obeying His commands and adhering to His prohibitions are basic matters, but they form the essence of the relationship between the Creator and His creation. Allah says:
"And I (Allaah) created not the jinns and men except they should worship Me (alone)." [al-Dhaariyaat 51:56]
Messengers were sent with one message: to tell their people "Worship Allaah, for you have no god besides Him."
Hence we may understand just how far short the person falls who believes that Allaah is one and does not associate anything with Him, but does not worship or obey Him, but rebels against Him and fails to follow His religion or Law, or the Revelation and Messengers which He sent for him and people like him. Does such a person deserve to enter Paradise or Hell?
This is the person who says: "I believe that there is One God Who created the universe, but I am going to stop there; I will not pray to Him or fast or perform Hajj or pay zakaat as He commanded. I am not going to carry out any duties towards Him; I will follow my own desires and do whatever I want, whether He permitted it or forbade it." Can such a person attain salvation on the Day of Judgement?
Allaah sent Messengers to every nation, that they might worship Him and shun false deities. The last nation is this ummah, and the last Messenger is Muhammad (peace be upon him). Allaah sent him for the whole of mankind, the entire world, and thus abrogated the previous laws and made this religion the best and most perfect and complete. Hence it is obligatory for everyone to enter this religion, for Allaah says (interpretation of the meaning):
"And whoever seeks a religion other than Islaam, it will never be accepted of him, and in the Hereafter he will be one of the losers." [Aal ‘Imraan 3:85]
On this basis, the fate of one who says "I believe in the idea of One God, but I do not want to be a Muslim, or I do not want to follow the last Revelation or the last Prophet," is clear.
Furthermore, the fate of an atheist, who rejects even the belief in God, is even clearer and more evident.
Finally, I hope that the matter is now clearer to you. I ask Allaah to guide us all to the truth and help us to follow it, for He is the best Supporter and Helper.