Bengali is the national language of Bangladesh, India and Singapore, and it's also spoken in Nepal and Malawi. Bengali was derived from Sanskrit, so there are similarities to Hindi.
What to expect when studying Bengali: no idea, I haven't learned Bengali yet. Please tell me your experiences with it, so that others can benefit from it.
Advice for learning Bengali: you really should learn the script, unless you plan to remain an analphabet in Bengali-speaking regions. Learning a foreign script doesn't have to be difficult, just be sure to memorise characters one at a time and practise as much as possible. Get advice valid for learning any language here.
Learn Bengali online and for free:
Course by virtual Bangladesh
Course: online book "Introduction to Bengali"
Bengali online dictionary
Professional (paid) translations from/to Bengali
Learn to write Bengali
Good materials for studying Bengali offline, from Amazon:
Teach yourself Bengali
A practical Bengali grammar
Lonely planet Bengali phrasebook
More from Amazon...
Misc resources, particularly for intermediate and advanced students of Bengali:
Bengali prose reader for 2nd year students
Tongue twisters in Bengali
Test your knowledge of Bengali
Learn how to curse in Bengli