I agree with #4. I think it would be more practical and cheaper to fly to Iceland (Reykjavik) and rent a car. I drove around the full circle in a normal car in April 2007. You can read all about it on my website, plus driving tips and Iceland-specific tips.
A few times I took the car on smaller roads and almost got stuck (see the dead end on my map on the Snaelfellsnes peninsula), but I don't think a Landrover or other 4x4 would have gotten me much further; it was 50 cm deep snow and so foggy that I could hardly see 1 meter ahead.
I really liked April as it was quiet, there was always room in gueshouses and hostels, waterfalls were beautifully frozen over, and I saw northern lights. Also, the days got longer and longer, after two weeks I already had a full hour of extra daylight in the afternoon (so probably two hours, including the morning). But some of the sights were not open yet or tours not running, for example the boats on Jökulsárlón iceberg lake only start in May, and dog sledding and things like that near Húsafell too. So I think May would be a perfect time to visit: still rather quiet and things are cheaper than peak season, but a bit warmer and perhaps some of the smaller roads will by then be accessible. Also, May is when the beautiful puffins come back on land after months out at sea.
A friend of mine had a small booklet with excellent info for hikes... so I guess if you go to a good travel literature / hiking shop you'll be able to find that. (For example "Pied a Terre" in Amsterdam.) In the Mývatn area you can make various walks and hikes onto craters and between huge lava sculptures, and from mud geyser to steam pit and so on, info can be found in the leaflet that you can pick up at Eldá guesthouse in Reykjalid. Skaftafell national park is another nice area for walks. And the area around Fljótsdalur hostel is great, you can walk a very deep canyon and reach a glacier. But basically you can hike all over Iceland, and even go on an ice climbing tour if you want.
Have fun,
Cécile
Travel tales, tips, photos and videos on my
website (Europe, Asia, Latin America, Africa)