The rental market has softened a little bit but it's not at the point where you'll easily find 'good deals'.
Things would be a little bit easier if you could increase your search area a little bit, Swansea, Seekonk, Barrington, Warren, Riverside, all these towns will still allow you to have a decently short commute to East Providence.
Wherever you rent though you should be able to find a decent 1 BR for 850 dollars or less. 2 BRs should range up to 1200 dollars, somewhat like your friend said, but you'll need to do a little bit of looking around.
If you do find a place, expect to pay first and security, first, last and security is not asked very often. I would definitely try various realtors, I used their services regularly and never had to pay a fee.
On the moving in early question I'd think a reasonable landlord would make an arrangement with you. But that's a case by case scenario so it's hard to answer.
Here's a link to apartment listings in the East Bay area in case you decide to take a look at those towns.
East Bay Classifieds | Real Estate
Good luck!