For sentiment classification of tweets, I have found that unigram, bigram features selected through information gain measure are effective. You may also include Hash tag information as a feature also.
Hey! You should have a look at the proceedings of SemEval (http://alt.qcri.org/semeval2015/cdrom/), maybe also consider 2014 and 2013. The participants investigated a lot of features for Twitter Sentiment Classification there.
In case of tweets that are generally grammatically incorrect sentences you have to consider the lexical specifics of tweets -- they can contain repetitions, inexact wordings, corrections etc. For classification I would consider stylometric features and probabilistic classifiers such as NB (see below).
Consider social aspects of the language of tweets' authors that can convey their sentiment in very different manner. For example, particular authors can mean a tweet as a positive joke and others can understand it as nasty rudeness.
I think whatever you do, it should include semantic analysis. Maybe you can use a conceptual ontology for languaje processing and also sentimental status recognition. Conceptual analysis can help you in understanding human behavior. Good luck!!
We done some seven variations test from 500 human raters on seven variations. This is the first and second paper about it, I am producing another journal writing and soon to be published, will update you if you interested. how about a cross country join research?