have taken an interest in the piano [...] I am considering buying a Casio LK-270 with 61 touch sensitive keys(which I hear is important)or a Casio CTK-541 to use to play for now
And How long do you think it would take without lessons to reach a point where I could play some songs relatively well?
Learning can take place without a teacher, but usually would occur at a very slow pace. There are some things you just cannot learn from books, they have to be shown to you by another person.
An small clarification (small but I think that it's very important): if you are going to practice in a 61 keys casio then you are not going to play piano, you are going to play keyboards. They are quite different. A piano has 88 keys and the way of play it is really different. It can be talked a lot about this but in brief, you must consider that the weight of the keys has nothing to do from one to the other.If by "songs" you refer literally to songs (playing, for instance, Beatles' songs), I think that you can play them in a very short time. How much exactly, I don't know, it depends on your talent, time available, etc. If you refer to classical music, this is a more complex question. I don't personally recommend self-taught systems to play the very demanding classical repertoire. But for the so called "light music" with no great pretensions, although not completely recommendable it's more sensible than with classical. The books by Roger Evans to play piano and keyboards are in my opinion reasonably good to start learning to play simple music in a short time but I insist: I'm not recommending in any way to be self-taught.I agree with you. I'd like to add that the risk is not only the slower learning process but the uncorrected vices and had habits which are very easy to be acquired but very difficult to get rid off.
To my knowledge it would take a year or two of lessons to really get anywhere?
A good teacher will have you going somewhere on your very first lesson.
There's a big, big difference between playing the keyboard and playing the piano.It's an unfortunate truth that doing the latter requires the down payment for a piano. If you look on Craig's List you can probably find an upright or a Clavinova fairly cheaply. If you can't read music, you probably need a teacher for at least a year or so.