You are worrying about nothing. All my replies above are accurate. The safest/easiest/smartest course of action is to forget it ever happened.
That said, assuming you have lots of time before your trip then go head and jump through the bureaucratic hoops. The only problem you face is that your incident occurred only 3 years ago. If you're unlucky enough to run into an official who's a dick then there's a small chance your application could be refused and then you'll really be screwed. If the circumstances are as you described though then the chances of that happening are small. It should be rubber stamped... but of course NOTHING is guaranteed when you're dealing with US Immigration.
ESTA is the Electronic System for Travel Authorization. http://www.cbp.gov/xp/cgov/travel/id_visa/esta/ It will cost you $14.00 to apply. It will tell you if you are a) approved and have no restrictions b) denied and need to apply for nonimmigrant visa at a US Consulate. Said it takes just a few minutes or if it is pending up to 72 hours (if there is a problem). As Cheers suggested....there is probably no concern, but you never know! I work really hard for my money and would hate to waste it on something that could of been prevented. Good luck. By the way...the US doesn't have Victorian law like you guys do. If you plead guilty it is a conviction...you are admitting to the crime. So unsure how they would view your situation. I think as long as it isn't a drug or sexual offense it probably isn't a problem.
bit of an update. had my visa interview a few days back. the consulate officer was sympathic with me. Requested a waiver from D.C.
so they're sending it off for me and itll be processed and hopefully itll be approved!!
Thanks for checking back in... it's always nice to hear follow up...