Answer
Salam Brother Khattab and welcome to Islam.
Thank you for your question and for contacting Ask About Islam.
Well, your top priority of course should be the Quran, I recommend the translation by professor M.A.S Abdel Haleem from Oxford University Press. I like it because it uses simple English and it has a great introduction with a brief history of Islam and excellent footnotes explaining many Islamic concepts.
You would also need to read the biography of Prophet Muhammad (peace be upon him) and his characteristics and how he lived; this is the blue print of how we should conduct our lives as Muslims.
There are many books under this category, I prefer you start with brief readings online then expand your knowledge using books as you go. Try starting with the section on this site called About Muhammad.
It would also be very enriching for you to read the experiences of other converts to Islam and listen to their lectures, their advice would be very useful to you because they know exactly what you’re going through as they’ve tried it themselves.
Google these names for books, videos and lectures: Dr. Jeffrey Lang, Dr. Murad Hoffman, Dr. Timothy Winter, he’s a professor at Cambridge so you might even be able to attend one of his lectures. Of course there are many others but this should be a good enough start for the next few months.
Try to get an idea of the Islamic history, not just politically but also in art, science and technology, medicine, agriculture, etc…; a good place to start is: Muslim Heritage
To be a better Muslim just simply apply what you read. That’s all it takes. When you read Quran or sayings of the Prophet (peace be upon him), just take time to think about the verses in relation to your life then follow the commands and avoid the prohibitions.
Make sure to do your prayers daily on time, and to find a few good Muslim friends to support each other in learning and practicing Islam.
Wishing you all the best and looking forward to hear about your progress.
Salam.