Let's us discuss the paths you have :
1-Self study path: you can start with Georgia weidman's great book
Penetration Testing: A Hands-On Introduction to Hacking
If you're interested in exploit development only, you can jump directly to the exploit development chapter in the book (which i -and i'm talking from experience - don't recommend ).
Next you can go with "Gray Hat Hacking: The Ethical Hacker's Handbook".
You can also use "The Shell coders' Handbook"
And finally, you can use Corlan's and FuzzSecurity's tutorials which are awesome.
2-Certificates' path :
A- SANS' : Assuming you don't have background in ethical hacking, i would recommend starting with SEC560 (Which is not directly related to ED) then move to SEC660 which is an indepth course on advanced Penetration Testing (including Exploit development) and finally you can move to SEC760
(Advanced exploit development)
Advantages : Indepth, good instructors , practical and you can take the training Online or onsite
Disadvantages : very expensive (compared to other courses ) and their exams are MCQ based
B-Offensive security :
You can start with OSCP which is penetration testing course with introduction on basic exploit development.
Then move to OSCE which is an exploit development and web hacking course
,and finally go for AWE which is an advanced exploitation course.
Advantages: hands-on training , pushes you to your limits , their exam's system is very interesting (you will have to hack machines in order to pass)
And finally , moderate prices.
Disadvantages : sometime you might find the course's offical material not enough and have to dig on your own , and the other problem is that not all the courses are available online.