Long tail keywords are useful if you are targeting localized results and for inner pages. But it is better to go with your generic core keywords for home pages.
I agree with Tessa. I would use a term that is slightly more competitive for my main keyword (and domain name). Then I would use the long tail keywords within posts and such. You should be fine this way.
A good quality post generally gets ranked on probably hundreds of keywords... many of them are long tail and some are short tail. Long tail keywords have less traffic... but the traffic is far more converting. On the other hand... short tail traffic is more... but may not convert that well. You need to come up with a mix of both types of keywords in your articles / content / posts
Long tailed keywords will have much less competition therefore it will be easy for you to rank for them quickly. Short tailed keywords have much larger competition therefore you would have to do more work in order to rank for them.