The dialects I have encountered are West Coast (kind of more slang heavy Midwest may even just consider it midwest), Midwest (kind of the normal), Southern, and North East (MA and NY but they sound different). Most Americans I know including myself really like Australian accents. That being said there is a lot of regional dislike of one another lol. A lot of Southerners are somewhat xenophobic and dislike North East dialects... and a lot of people don't like Southern accents and consider the speakers to be less educated (even in the south), if you meet someone who says y'all they are likely from the South =]. Also the key I would think to fitting in on normal conversations with Americans would be to not be "too" formal, most of us are pretty laid back I think. Personally I don't like North East accents and I prefer to speak with a more midwestern sound, but I've been told I have a "professional" tone. A lot of the time people who speak with certain word choices are viewed differently, for example most people like it when others show confidence and interest. So the words "That's interesting" and "I definitely can" convey a tone of wanting to learn and being a confident person. The opposite for those would be "Ok, whatever" and "I don't know...". Also there are a lot of region specific slangs and preferences, personally I dislike the Massachusetts accents and I love Australian accents. The best middle ground is Midwest I would say. I've worked as a customer service manager speaking to thousands of people for Verizon Wireless where word choice really mattered. Also I have lived in California (West) , Michigan (Midwest), and Kentucky(South/Midwest).

I'm by far no expert, but for me, 3 main accents in the States come to mind: Yankee/New England (New York, Philly, Boston, etc.), Midwestern (Chicago, Minnesota, etc.), and Southern (Alabama, Georgia, Mississippi, etc.). Of course, these people would probably scream knowing I put them in the same categories, but I can tell the slight difference between, say, someone from Philly and someone from New York. I'm from Florida and (of course) I don't think I have an accent ;). If I were you, I'd go for British!

There are countless accents in America, I wouldn't even be able to tell you what the most common is because that would be way too subjective, there's places separated by barely a few miles, yet they speak with completely different accents. Also, let me give you a very good piece of advice: Do not focus yourself on accents. This should be your last step towards perfection, when you are already fluent in a language. As a matter of fact it should come after fluency! Once you are fluent you should first focus on accent reduction, meaning getting rid of your native language accent, once that has happened you will naturally pick up the accent of where you live over time.