Yes an engineer graduate can apply for bank exam.
For applying for bank exam, you only need to complete your graduation from authorized university, It doesn't matter from which stream you are , you are eligible for bank exam.
Yes , Bank Exam is good career choice for engineer, i.e, if you are interested in it. Career choice can not be decided on the basis of stream , it only depends on your interest. Sometimes an MBA student gives up his career to pursue their career in Sports because he is interested in sports not in MBA.
Banks is one the industry which is growing rapidly.Getting a bank job is a matter of prestige, especially in a government sector.So remove that though that it is for you or not , It is a well reputed job.
A salary of a bank is different at different posts.After 7th Pay commission salary of Bank PO will be around 40K. It varies according to the banks.It is good start for a fresher.
You are a engineer but you did not mention your branch so I can not tell you much but you can also go for IBPS SO which provide you a great career path in your specialized field. If you are from CS branch than you can make your career ahead in IBPS SO IT Officer.
You can give the following exams
1. IBPS PO
2. IBPS Clerk
3. IBPS SO
4. SBI PO & Clerk
5. Other bank exam which is conducted by their own.
Hope all the doubts have been cleared of all the candidates about bank exam.IBPS PO exam is about to come in October . All the best for your IBPS PO Preparation