I don't use Lightroom but there are several answers addressing how to use Lightroom for that purpose. Let me address more general aspects of your question.

You probably are sending JPEG files to your editor unless your editor has specifically requested another format. There are two things that make a JPEG file big.

An important factor is the number of pixels and many cameras today will provide more than you likely need; you should reduce the image to whatever is appropriate. If the image is to be printed in a high-class glossy magazine then you will probably need many more pixels than if it is to be printed in a newspaper. Discuss with your editor what dimensions in pixels are needed and reduce your image dimensions appropriately.

The second issue is the compression factor. When you save a JPEG file you will probably find a menu to adjust the compression factor (and possibly a check-box for whether or not to compress). You probably do want to compress the image unless it is to be edited and re-edited later - again, ask your editor what he or she wants. Be aware that compressing the image will reduce the quality - though you probably will not see the difference with only a small amount of compression and even with a large amount you may have to look very carefully to see the difference.

I just got the canon e-mail myself yesterday. I've been debating getting a p/s or bridge to take along with me on a 2-week overseas trip next year rather than taking my DSLR kit (or most of it) and saving weight (I can buy more souvenirs and save my neck). Let me know what you think of it. I've seen some good reviews. Also thinking about a Sony. I still have a vast majority of my trip to pay for yet, though so I probably won't get one right away. Not including the airfare it's $2,800! It will be the longest trip by 4 days and by far the most expensive, but going to the Holy Land is on my bucket list.