Well, I don't know too much about publishers in your country or my own, but let me tell you about what I know about Japanese ones. I think you should try out for "gensaku" where people with original idea make others draw for them. There are very few opportunities for gensaku, but there seems to be some contests in manga magazines if you are interested. However, according to some, you'll have to draw some rough sketch of your story(called ne-mu or "name") to give the editor some ideas. For people trying out for manga-ka, they will have to draw it on B4 paper with A4 as the drawing space. It might be same for gensaku so you might need to check that out on magazines.
DON'T SEND YOUR DRAWING ON A NOTEBOOK OR A NORMAL PHOTOCOPY PAPER!!
Draw on designated manga paper! For doujinshi (where you will self publish so, you will go to the printing company or doujinshi magazine company), use A4 sized "doujinshiyou genkouyoushi". For submitting to a pro manga magazines, use B4 sized "toukouyou (for submission) genkouyoushi". They are slightly thicker and more durable than a normal photocopy paper. You can make them yourself, but I suggest you buying it since it will be less work and mess. The pale blue lines and rulers on that paper will help you draw koma easier. The lines are blue since if you photocopy the paper, it won't appear on the copy. However, it's different in the case of scanning.
The rules are different for CG mangas since you will have to give CD with the graphic files saved in 1200 dpi monochrome photoshop format along with printed pages (according to one publisher). In this case, it can be printed on a normal A4~B4 sized photocopy paper. However, as I mentiond before, rules are diffrent for each company.
Well, that's the case for Japanese publishing companies. It will be different for other countries, so check it out yourself.
In addition, contests usually require X8 pages. 8, 16, 24, 32 pages for example. 8-16 pages for short story, 4-koma mangas. 24-32 for an one-shot chapter. They use multiples of 8 since it's easier to arrange them into a magazine.
If you are trying it out in Japan, I suggest you make an appointment by phone or mail at least 2 weeks prior to meet the editor in person or sending it to a contest. It's something that anybody can sign up (usualy above 15 years old), but you will need to know Japanese and your work has to be in Japanese up to the point where you can write slangs and dialects. Meeting with the editor will allow you to have an intensive advice (up to the point that you want to get a voodoo doll) but it can be short(just a few minutes) if the editor is bad or not interested in your work. Some suggest visiting several publishing companies, but like I, some choose to visit just one that seems to fit your manga the best. Each magazine have different theme, so study beforehand about it or else your work will be rejected just because it's in a different genre. Since you will be visiting an editor who might be your future boss, you will have to wear semi-formal clothes (no jeans) and present your work in an organized manner (I suggest binders with clear pockets). That way, if they think that your work is good enough to get published, you can just hand it in. If you are visiting several companies on a same day, show them the work and say that you will be sending the file by mail later (i.e. post mail and not e-mail. They usually don't accept work attached to e-mails). However, they can point you out clearly about what is good and bad in your work. Japanese editors are notorious for being harsh to first timers so, don't feel bad if they say stuff that you don't want to hear. They are really busy with their work (I had to wait an hour past the appointment time) so just be glad that they took a few minutes of their time to take a look at (or more like flip through) your work.
Oh, and another thing. They will talk in manga vocabs so you will need to know key words such as "komawari", "uchiwaku", "tachikiri" if you are trying it out in Japan. I think you will need to learn anyway in your language even if you are trying it out in your own country. It's just a vocab used in printing companies, so search the web or books to get familiar with it.
As for the contest, it will allow your work to be seen by several editors and pro-mangaka. Therefore, it's good if one of them likes it, but the comments will be brief. I haven't tried out for one yet, so I don't know personally, but comments will be pretty strict as well in order to point you out in a right direction. Most people send multiple times and only a few get accepted, so the competition would be very rigorous. Despite that, it will be a good experience ; )
I also suggest you looking into on-line manga groups who are willing to draw for you or just get tips.
If you have any questions, please feel free to PM me