IreneCroft
If the goal is to cover as many different topics as possible then I would recommend following books:
1. The Complete Tarot Reader: Everything You Need to Know from Start to Finish - Teresa Michelsen (with practical exercises and a lot of theory. It helps to see the system behind the Minors and the Court. Plus: different layers of the Majors (psychology, archetypes and more) and advices how to read for yourself and others)
2. A Guide to Tarot Card Meanings - Mark McElroy (it's in public domain, so you can download it for free: http://www.tarottools.com/a-guide-to-tarot-card-meanings/ There's a lot of information: Keywords, Range of Meaning, Correspondences, Advice, Symbols and Insights, Questions to Ask)
3. The Tarot Handbook - Hajo Banzhaf (general meanings of the cards and their meanings in positions of the Path Spread so you get clues for how to interpret cards in different layers - somehow very close to Body-Mind-Spirit)
4. What's In the Cards for You?: Test the Tarot - Mark McElroy (it's just a lot of fun to read! And by the way it introduces many ways of using the cards. I almost forgot! It's not plain theory but daily experiments. So the whole practical course takes 30 days. In the end you understand how you prefer to use the cards)
5. Tarot Journaling: Using the Celtic Cross to Unveil Your Hidden Story - Corrine Kenner (everything you need to know about Tarot Journaling)
6. Tarot Tips - Ruth Ann Amberstone and Wald Amberstone (a lot of useful information on different topics)
7. Tarot Spreads: Layouts & Techniques to Empower Your Readings - Barbara Moore OR Designing Your Own Tarot Spreads - Teresa Michelsen (both books are about designing your own spreads but the first one has more author's spreads)
8. The Complete Book of Tarot Reversals - Mary K. Greer
9. Understanding the Tarot Court - Mary K. Greer and Tom Little
10. Tarot Wisdom: Spiritual Teachings and Deeper Meanings - Rachel Pollack
As for history of Tarot there's a lot of information online (try http://tarot-heritage.com/ or http://forum.tarothistory.com/). So if you're "on a limited budget" this kind of books can wait for some time. The same goes for 365 Tarot Spreads by Sasha Graham. I love that book but i don't think it's a "must-have" one.
1. The Complete Tarot Reader: Everything You Need to Know from Start to Finish - Teresa Michelsen (with practical exercises and a lot of theory. It helps to see the system behind the Minors and the Court. Plus: different layers of the Majors (psychology, archetypes and more) and advices how to read for yourself and others)
2. A Guide to Tarot Card Meanings - Mark McElroy (it's in public domain, so you can download it for free: http://www.tarottools.com/a-guide-to-tarot-card-meanings/ There's a lot of information: Keywords, Range of Meaning, Correspondences, Advice, Symbols and Insights, Questions to Ask)
3. The Tarot Handbook - Hajo Banzhaf (general meanings of the cards and their meanings in positions of the Path Spread so you get clues for how to interpret cards in different layers - somehow very close to Body-Mind-Spirit)
4. What's In the Cards for You?: Test the Tarot - Mark McElroy (it's just a lot of fun to read! And by the way it introduces many ways of using the cards. I almost forgot! It's not plain theory but daily experiments. So the whole practical course takes 30 days. In the end you understand how you prefer to use the cards)
5. Tarot Journaling: Using the Celtic Cross to Unveil Your Hidden Story - Corrine Kenner (everything you need to know about Tarot Journaling)
6. Tarot Tips - Ruth Ann Amberstone and Wald Amberstone (a lot of useful information on different topics)
7. Tarot Spreads: Layouts & Techniques to Empower Your Readings - Barbara Moore OR Designing Your Own Tarot Spreads - Teresa Michelsen (both books are about designing your own spreads but the first one has more author's spreads)
8. The Complete Book of Tarot Reversals - Mary K. Greer
9. Understanding the Tarot Court - Mary K. Greer and Tom Little
10. Tarot Wisdom: Spiritual Teachings and Deeper Meanings - Rachel Pollack
As for history of Tarot there's a lot of information online (try http://tarot-heritage.com/ or http://forum.tarothistory.com/). So if you're "on a limited budget" this kind of books can wait for some time. The same goes for 365 Tarot Spreads by Sasha Graham. I love that book but i don't think it's a "must-have" one.