Todd,
If you want to get a Grip & Grin style shot with you holding the fish I suggest getting a Gorilla Pod tripod.
http://joby.com/gorillapod/original/
It is a cheap and very functional option when fishing on your own. Keep your camera attached to the tripod, set it up while fighting the fish or once you have landed it, keep the fish in the water, set the camera on its timer, and lift the fish out of the water just prior to the camera taking the picture. I’ve gotten the best results leaving my camera on auto settings as apposed to any of the selectable setting options.
Alternatively, for shots of just the fish, there are nearly limitless options. IMO, keeping the fish in the water produces better pictures, and it’s obviously much healthier for the fish. Play around with different perspectives and get an idea of what you like. Using your rod/reel in the shot is an often-used way to give reference to the size of the fish. Also, if you plan to take pictures of the fish in the net, it can be worth investing in a net that photographs well (i.e. nice wood frame). Taking macro shots of specific parts of the fish like the head or fins is another option that is an easy way to photograph your fish when alone.
Re: cameras, I have an old Pentax w30 and it has yet to let me down. I know a lot of people that really like their Olympus waterproof point and shoot as well.
Good luck,
Tim