You indicate you want to present the songs after you record them for your album. A fundamental thing you need to determine - do you want to promote yourself as a songwriter or as an artist (ie: singer/songwriter). These are two completely different approaches.
The Songwriters Market is a good book which identifies producers, managers, record companies, etc. I recommend it to anyone who is really serious. Another decent book is (I may have this title a little wrong) 88 Songwriting Mistakes and How To Correct Them. Candidly, there are numerous well writen books on the subject - and anyone who is serious about trying to "pitch" songs would be a fool not to read as many as possible. While asking a few questions on this or some other web site is not a bad thing - you are not doing justice to yourself if you fail to complete some serious research.
When submitting to a publisher, you must first determine if the publisher works in the genre you write in (submitting a country song to an R & B publisher is a waste of everyones time). You also need to know if the publisher accepts unsolicited material (if they do, they may not be a serious contender) or what format they want submitted, etc. As a general rule of thumb, you need to make contact to introduce yourself and establish a rapport with someone before mailing a CD (never send a demo to "to whom it may concern").
Regarding if a demo should be full band vs. piano/voice - while this has always be a subject of debate the fact is (and I have discussed this with two publishers I work with and others in the industry) these days, everyone has access to quality recording gear and candidly, publishers expect a fairly well arranged, well performed, demo (at least guitar/keys, base, drums, and of course vocals). In fact, one of the publishers I work with provides "source material" to film and TV industries and he will only accept master quality product.
The days of the simple guitar/piano with vocals are long gone (unless you are marketing that type of song). Now there can be a fine line between a well produced demo and a master quality recording - and one must be careful not to over produce, however, with no exception - make certain you have the best vocalist you can afford (rule of thumb a quality vocal will cost about $100 per song - and it's worth it if you really want the demo to standout).
For whats it's worth, I have had songs published and placed in movies and on artists recordings (nothing of any significance, no major theatrical releases and no "name" artists - but enough to bring in some quarterly checks from BMI and/or publishers. Even with what is the start of a "track record" I still have to submit the best written, best sung, best recorded material each and every time. My publishers will ignore me just as much as someone in the door for the first time if I don't present the very best I can (which amounts to maybe 2% of all that I've written).
I made a lot of mistakes in the beginning - I tried to sing on my demos, I played all the parts, I sent out unsolicited tapes, etc. etc. Candidly, I wasted a lot of time, money and damaged my credibility by failing to really understand the right way to promote myself as a writer. Many of the mistakes were because I was too ignorant, too lazy and perhaps to overly self confident to realize that I needed to research.
Only after I began to do research, joined a songwriter organization and tried to learn (rather than simply thinking I was hot shit) did I actually start to see some positive results. In fact the more I worked with other writers and did more research the more I realized I was not hot shit and that there were a lot of people way more talented than I (and I'm considered an A list player in the mid sized metro area I work in - with plenty of gigs and studio work))
I share this so that perhaps you can learn from my mistakes.