Safest approach I have found is Bracket, Bracket and Bracket again. The sun is just to damn bright and tends to make a mess of auto metering.

As for getting it to be a focused clean circle of sunnyness. hhhmmmm make sure you lens and filters are squeaky clean to avoid and flare and distortion of the sunlight. Even then I think it will be a lot of wish full thinking and some Photoshopping afterward. I would suggest leave it as it is. Everyone knows what it is and can accept that it may not be perfect. It can be distorted by the heat distortions in the atmosphere, high clouds, smog and other various atmospheric annoyances. Concentrate on getting the rest of the shot as good as you can and leave the sun as it is.

If you wish to photo the sun itself. DON”T throw a monster lens on and try. If your not careful you may damage your eye and may damage your camera too. You only have two eyes, (assuming you have not lost one already), so try not to damage them for some thing so trivial.
Go to a astronomy group and talk to them about solar observing and photography.

We have in fact recommended using a tripod. Hand-holding is a personal preference – generally I tend to hand-hold for as low as 1/15th and count on my VR lens which gives me acceptable results (do read Ken’s excellent post on this – “Digital Killed My Tripod“). Most of the people never view or use photographs at 1:1. However viewing at 1:1 does enable you to criticize the sharpness no matter what the equipment used. If you are shooting for a photography magazine, by all means use a tripod and even a wireless remote trigger to avoid any vibrations introduced by the touch of the shutter-release :).

As for your shutterspeeds for handholding – you are way off. 1/20? rule of thumb says inverse of focal e.g. 50 mm lens would give a lowest speed of 1/60, 200 mm 1/250 etc. Now this is increased if the camera sensor is smaller than the standard 35 mm size e.g. Nikon dx cameras where say a 200mm gives an 35mm equivalent of 300mm. In this case the 300 is the figure used which puts one in the 1/500 range.

Now you may be able to get pin sharp at 1/20 but I very much doubt it – if you don’t believe me look at images taken at 1/20, by yourself, with and without a tripod at 1:1 on a screen and tell me that you don’t notice a difference.

A lot of things in photography are open to preferences of the photographer but here you are straying way outside the normal parameters and if someone who is relatively new to DSLR’s were to read your post they would wonder why they were not getting good results.

Absolutely mesmerizing , and a gift to be able to walk along and look for sea turtles that grace our oceans. It is so peaceful and healing.