Unfortunately "secure" is a relative term. Seeing a picture on a monitor means that a local copy exists on the PC, no matter how you swing it.
Nothing can stop anyone from using a screen-scraper to save an image they can see.
But, there are some precautions one can take. For example: don't store full-size images anywhere - just versions large enough to fill the monitors of your legitimate viewers. a 24" wide is 1920X1200 - a mere 2+ Megapixels.
If you want certain people to be able to download full-size versions of your image, you can use file-hosting services without indexing such as rapidshare - but you will then not have everything (ability to view and download) in one place.
When I went through the same considerations as you and looked at all the options, I found that the best combination for me was smugmug. There is an annual fee, but it has great galleries, very fast, unlimited storage and adequate flexibility and gives you your own personal URL and you decide if you are "searchable" .
Good luck with your choice!