To be familiar with Islam and Shia, you should read the following books:
The holy and central religious text of Islam, a revelation from Allah, the Exalted. Unlike Torah and Gospel, Quran is not changed during 1400 years and nowadays all Muslims (Shia and Sunni) have the same Quran.
Daily reading of this book is advised in Islam and almost every Muslim has at least one Qoran in his home. Quran is in Arabic, but its translation in English and other languages is available at Tanzil.net
Some verses of Quran:
وَقَالَ رَبُّکُمُ ادْعُونِی أَسْتَجِبْ لَکُمْ
اللَّـهُ لَا إِلَـٰهَ إِلَّا هُوَ الْحَیُّ الْقَیُّومُ ۚ لَا تَأْخُذُهُ سِنَةٌ وَلَا نَوْمٌ
Allah - there is no deity except Him, the Ever-Living, the Sustainer of [all] existence. Neither drowsiness overtakes Him nor sleep. Sura Baqarah, Verse 255
فَاقْرَءُوا مَا تَیَسَّرَ مِنْهُ ۚ وَأَقِیمُوا الصَّلَاةَ وَآتُوا الزَّکَاةَ وَأَقْرِضُوا اللَّـهَ قَرْضًا حَسَنًا ۚ وَمَا تُقَدِّمُوا لِأَنفُسِکُم مِّنْ خَیْرٍ تَجِدُوهُ عِندَ اللَّـهِ هُوَ خَیْرًا وَأَعْظَمَ أَجْرًا ۚ وَاسْتَغْفِرُوا اللَّـهَ ۖ إِنَّ اللَّـهَ غَفُورٌ رَّحِیمٌ
So recite what is easy from it [Quran] and establish prayer and give Zakah and loan Allah a goodly loan [help poor people]. And whatever good you put forward for yourselves - you will find it with Allah. It is better and greater in reward. And seek forgiveness of Allah. Indeed, Allah is Forgiving and Merciful. Surah Muzammil, Verse 20
یَا أَیُّهَا الَّذِینَ آمَنُوا کُونُوا قَوَّامِینَ بِالْقِسْطِ شُهَدَاءَ لِلَّـهِ وَلَوْ عَلَىٰ أَنفُسِکُمْ أَوِ الْوَالِدَیْنِ وَالْأَقْرَبِینَ
O you who have believed, be persistently standing firm in justice, witnesses for Allah, even if it be against yourselves or parents and relatives. Surah Nisa', Verse 135
یَا أَیُّهَا الَّذِینَ آمَنُوا اسْتَجِیبُوا لِلَّـهِ وَلِلرَّسُولِ إِذَا دَعَاکُمْ لِمَا یُحْیِیکُمْ
O you who have believed, respond to Allah and to the Messenger when he calls you to that which gives you life. Chapter Anfal, Verse 24
Islam Opinion About Mary
فَأَجَاءَهَا الْمَخَاضُ إِلَىٰ جِذْعِ النَّخْلَةِ قَالَتْ یَا لَیْتَنِی مِتُّ قَبْلَ هَـٰذَا وَکُنتُ نَسْیًا مَّنسِیًّا ﴿٢٣﴾ فَنَادَاهَا مِن تَحْتِهَا أَلَّا تَحْزَنِی قَدْ جَعَلَ رَبُّکِ تَحْتَکِ سَرِیًّا ﴿٢٤﴾ وَهُزِّی إِلَیْکِ بِجِذْعِ النَّخْلَةِ تُسَاقِطْ عَلَیْکِ رُطَبًا جَنِیًّا
"And the pains of childbirth drove her to the trunk of a palm tree. She said, Oh, I wish I had died before this and was in oblivion, forgotten. (19:23)
But he -Gabriel -called her from below her, Do not grieve; your Lord has provided beneath you a stream.(19:24)
And shake toward you the trunk of the palm tree; it will drop upon you ripe, fresh dates. (Suraat Mariam 19:25
Several Quranic software for Windows, Linux, Android, iOS and other platforms are available and you can take them from Google Play and other App stores.
2. History of Islam
Every nation and religion has a history behind it and reading the history is very important for us to have a background of Islam. It also prevents us from making similar mistakes, previous Muslims performed. There are a lot of historical books and we can not say which one is better, but in Al-Islam.org
you can find several historical readings
. However, several historical documents are cited in Quran and Nahj-al-Balagheh
3. Nahj al Balagha
Nahjul-Balagha (The Method of Eloquence) is a book gathered by Seyyed Razi from Sayings and Sermons of Imam Ali. Its eloquence is on top of all other Arabic books except Quran. Reading this book, you will be more familiar with Imam Ali (AS) the first Imam after the Prophet (SAWA). The following links are online version of Nahjul-Balaghah
Letters and Sayings
4. Mafatih Al Janan Dua's (Supplications)
Islam and specially Shia, have a lot of holy texts taken from the Prophet Muhammad (SAWA) and his Ahle-Beyt (Fatima and 12 Imams). Some of them are in the form of Dua (supplication). These are not obligatory to be read in a regular manner, but reading Dua make a pleasant feel and we usually think we are more near with God after reading Dua.
The book Mafatih-Al-Janan
(Keys of The Heaven) is the most popular book in Shia community so that almost all Shia Muslims have a Mafatih
in their home and read some of it's Duas in special times.
As a shia Muslim, you must follow a Grand Ayatollah (a religious expert with special conditions) to perform your religious doing (secondary principles) according to his Fatwas. For example these are two Fatwas from Imam Khamenei
Q: There are some dead cells of the skin that at times fall off from the hands, lips and feet. Are they pure or najis?
A: The fine skin that separates by itself from the hands, lips, feet or any other part of the body, is pure.
Q: What rule applies to university students who travel beyond the shar'i distance at least two days a week for the sake of studying?
A: A trip for study is not considered as working trip. It is obligatory on them to shorten their prayers, and their fasting is not valid, unless they intend to stay there for ten days.
You can find complete list of Fatwas here: Fatwas of Imam Khamenei
Reference: Shia Muslim