Reddit reviews A Primer For The Mathematics Of Financial Engineering, Second Edition (Financial Engineering Advanced Background Series)

You already have a great foundation. Most who start trading or are even remotely interested in it, don't appreciate the value of statistics in finance, of all professions.

1. The book Forecasting by Makridakis is specifically focussed towards students of business/finance. It is quick and easy to read, and reaches to the meat of the subject (ARIMA stuff) pretty quickly (you can skip or quickly read through the introductory chapters). You can pdf version on scribd. There is another book, Mathematics of Financial Engineering, which provides a more mathematical overview of various financial instruments (eg bonds, options, futures, forwards). Some other books I mention here that's worth reading for trading, but you might know most of it with your background.
   
   
2. I go with Forex, EURUSD specifically simply because: huge volume (trillions worth transaction per day), some specific parameters to follow (interest rate, central bank mandate, gdp, inflation, purchase manager indices), a comparatively easier intuitive assessment (you can get an idea of investor sentiments by looking at the economic indicators/central bank statements). Whether it should be spot FX or futures FX is something to decide: people might prefer futures because there is a central exchange, more transparency.
   
   
3. You can get all the data you need by getting a MT4 platform from your choice of broker. You don't need to pay for it, or even have a live account. Just open a demo account and you will have access to historical data.
   
   
4. MT4 is the most widely used platform. You can write programs for it too (Expert Advisors execute tick-by-tick operations; there are scripts and custom indicators too). The programming language is MQL4, which has a syntax very similar to C/C++, so it's easy to adapt to it.
   
   Best of luck!

what specifically are you interested in?

https://www.quantnet.com/threads/quantnet-best-selling-books-of-2012.12190/

https://www.quantnet.com/threads/master-reading-list-for-quants-mfe-financial-engineering-students.535/


http://www.nuclearphynance.com/Show%20Forum.aspx?ForumIDKey=8

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http://www.cs.sunysb.edu/~skiena/691/

http://developers.opengamma.com/quantitative-research

http://www.thalesians.com/finance/index.php/Reading_List

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http://www.amazon.com/Primer-Mathematics-Financial-Engineering-Second/dp/0979757622/

commonly heard: "Just read Hull OFOD" http://www.amazon.com/Options-Futures-Derivatives-DerivaGem-Package/dp/0132777428/

http://www.amazon.com/Stochastic-Calculus-Finance-Binomial-Textbooks/dp/0387249680/

Most programming for financial engineering will be in C++, Python, R, or MATLAB; some books written by Mark Joshi or Daniel Duffy may be a good place to look for how C++ is used in FE (Duffy also has an online C++ course that's quite good).

If you have a physics/math background then you likely have 90% of the required maths, such as calculus, linear algebra, probability and statistics. I would recommend taking a course/reading a book on advanced probability, real analysis, and stochastic calculus, but these are not trivial subjects. If you are more interested in learning specifically about how math is applied to FE you can take a look at a book such as a primer for the mathematics of FE.

Also, check out online forums that discuss this such as quantent.

https://www.amazon.com/Mathematics-Financial-Engineering-Advanced-Background/dp/0979757622

More of a intro to the math/finance used in an MFE course, but this is a great book. http://www.amazon.com/Mathematics-Financial-Engineering-Advanced-Background/dp/0979757622