most illustrators i know send postcards to companies/editors/artdirectors that they've never worked with before (and those that they have worked with, to keep them fesh in everyone's mind). you can get postcards printed many many different places. www.americanpostcard.com
is a popular site i think, though i've never dealt with it before. the contents of the postcard are very simple. there's always an image on the front of an illustration that you choose to represent yourself with and contact info on the back. actually, as long as all of that info is there, it doesn't really matter where you put it.
postcards are good because they can't HELP but see the image. it's right there in their face the instant the postcard is near them. whereas if you send something in an ENVELOPE it has to be a pretty darned fascinating envelope to get them to open it.
you'll also want a portfolio. if they like how your work looks on the postcard the next step is usually a phone call from them to set up a portfolio reveiw. i don't know, they may just give you comissions.
generally, i've heard that emailing is NOT such a good idea. these people are totally swamped with emails and if they don't recognize the address, the odds are not in your favor of it being opened.
i know that hallmark has a website. you can find submission guidelines there. i had a prfessor who worked for them full time for a while. they supply materials mostly, but they also own any ideas that you produce while working there! i don't know how far they go with that, but i'd be leary. i think most companies like hallmark have rules like that.
as far as what to charge, i'm confident that the "Graphic Artists Guild Handbook: Pricing & Ethical Guidelines" will give you what you want to know. every job is different and you'll find them ALL in this book. as well as tons of other very helpful information like contracts and such. i can't recommend this book enough. www.gag.org
as a freelance illustrator, you wouldn't have much stability and job security of course. but you can get jobs as a staff illustrator some places. hallmark is one such place. but first you have to get hired! children's text books are known for having long term jobs as well i think.