I use flickr (which is free for up to 200 photos and then something like $20 a year for an unlimited amount, which is pretty good - I prefer it to deviant art and have used both in the past) to store my photographs and artwork, and have a separate portfolio site, where I can show it off properly. Flickr works a bit like an online sketchbook, and I use it to store photos of friends and family etc. as well.
The benefit of having a flickr account is that you get an awful lot of storage space. I don't have any images actually stored on my webspace, I put the images from flickr on my website (there's a little code at the bottom of flickr images that you can just copy and paste, each image on your website will take you to its flickr page when clicked on - but I quite like that as there's a space for people to comment on your pictures).
I agree that if it's a portfolio site, showing off the pictures you are most proud of is the best idea. Designing the page so that the colours, graphics, font etc suit your artwork rather than the generic deviant art/flickr/etc. websites gives it a more professional look too.
I have a link to my flickr account on my portfolio site so that anyone who likes the images they see on my website can have a look at more.
(There are also scripts you can install yourself on your website that give you little galleries, for example Simple Viewer (http://www.airtightinteractive.com/simpleviewer) that you can see in action on magical artist Molly Lesher's website (http://www.mollylesher.com). If you aren't too sure about codes and technical stuff though, it's easiest to leave it to big websites like Flickr.)
Did that make sense? I've been doing the portfolio site thing for a good long while and have tried most methods. Looking at how other people arrange their art is helpful too.