Will it improve my credit score and help my ability to buy home later if I pay my rent 30 days early for the next two or three years?
No. Your landlord probably isn't going to report early payments to the credit bureaus. Just make sure you pay it on time. It is smart to pay a few days early, though - maybe seven to 10 days ahead of time, but for a different reason. That way, if something goes wrong at the bank, you've still got time to fix the problem. Chances are your credit score won't be impacted by your rental payments unless you're late, and especially if you have several late payments. That could sure become a black mark against you later!
I'm not a big fan of the FICO score, because it doesn't measure things like assets, income or net worth. It's really just an indicator of your interaction with debt. This is one of the reasons why it's really dumb for companies to base lending decisions solely on a FICO score.
Fortunately, you can still find lenders that provide mortgage loans based on manual underwriting procedures. But they're getting harder and harder to find!